5757 S. University Ave.

Chicago, IL 60637

Main: 773.702.5599

bfi.uchicago.edu

WORKING PAPER · NO. 2018-74

Rebel Capacity and Combat TacticsKonstantin Sonin and Austin L. WrightMARCH 2020

Rebel Capacity and Combat Tactics∗

Konstantin Sonin and Austin L. Wright†

March 23, 2020

Abstract

Classic and modern theories of rebel warfare emphasize the role of unexpected attacksagainst better equipped government forces. We test implications of a model of com-bat and information-gathering using highly detailed data about Afghan rebel attacks,insurgent-led spy networks, and counterinsurgent operations. Timing of rebel oper-ations responds to changes in the group’s access to resources, and main effects aresignificantly enhanced in areas where rebels have the capacity to spy on and infiltratemilitary installations. Results are supplemented with numerous robustness checks aswell as a novel IV approach that uses machine learning and high frequency data onlocal agronomic inputs. Consistent with the model, shocks to labor scarcity and gov-ernment surveillance operations have the opposite effect on attack timing. In addition,we investigate the impact of attack timing on battlefield effectiveness and find thatit reduces soldier efficiency during missions to ‘find and clear’ roadside bombs andincreases bomb-related casualties to government troops.

∗For advice and comments, we thank Karen Alter, Peter Deffebach, Quy-Toan Do, Kai Gehring, GaranceGenicot, Michael Gilligan, Matthew Gudgeon, Amanda Kennard, Susan Hyde, Michael Kofoed, DanielKrcmaric, Dorothy Kronick, Sarah Langlotz, Francois Libois, Nicola Limodio, Andrew Little, John Loeser,David Mansfield, Luis Martinez, Aila Matanock, Michaela Mattes, Marc Meredith, Owen Ozier, Kyle Pizzey,Michael Povilus, Robert Powell, Martin Ravallion, Peter Rosendorff, Arturas Rozenas, Mehdi Shadmehr,Alexander Stephenson, Oliver Vanden Eynde, Juan Vargas, Duncan Walker, Alex Weisiger, Liam Wren-Lewis, Andrew Zeitlin, and Yuri Zhukov and seminar participants at Columbia University, GeorgetownUniversity, Northwestern University, UC Berkeley, University of Pennsylvania, and The World Bank Re-search Group. Faculty at the United States Military Academy (West Point) provided exceptionally detailedfeedback. This material is based in part upon work supported by the Pearson Institute for the Study andResolution of Global Conflicts. We thank Jarnickae Wilson for his important contributions to early ver-sions of this paper. Eli Berman, Ethan Bueno de Mesquita, and Jacob Shapiro are owed a particular debtof gratitude for their support of this and related projects. Maria Ballesteros, Connie Guo, Lana Kugli,Michelle Liang, Mariya Milosh, Yonatan Litwin, Paul Soltys, and Julian Waugh provided excellent researchassistance. All errors remain our own.†Harris School of Public Policy, The University of Chicago, Chicago, IL 60637. Emails:

ksonin@uchicago.edu and austinlw@uchicago.edu.

Attack [the enemy] where he is unprepared,

appear where you are not expected.

Sun Tzu, “The Art of War”, 5th cent. BC

1 Introduction

Intrastate conflicts have replaced interstate wars as the main source of human loss and

population displacement. Generally, it is well understood that resource endowments shape

how rebels recruit, retain, and deploy their fighters (Weinstein, 2007). Fluctuations in rebel-

held economic resources affect the scale of insurgent activity (Dube and Vargas, 2013),

their control of strategic territory (Kalyvas, 2006), and how they treat civilians (Wood,

2014). These factors, in turn, impact whether civilians cooperate with rebels or collude with

government forces (Condra and Shapiro, 2012) and the ability of the government to engage

in development and reconstruction (Sexton, 2016). Shocks to rebel capacity impact even the

finest aspects of internal warfare.

One central question that remains largely unexplored is whether rebel capacity influences

actual military tactics, i.e., how rebels fight. In particular, classic theories of insurgency

note that the rebel’s main advantage in an asymmetric conflict is the ‘element of surprise’

(Galula, 1964). If guerrillas aim to undermine their more powerful rivals, their attacks

must be unpredictable and, as such, difficult for government forces to anticipate and thwart

(Thompson, 1966; Powell, 2007a,b). Yet the strategic value of random combat may diminish

as rebels accumulate resources. As their capacity grows, rebels may shift from guerrilla

tactics to conventional warfare, where frontal assaults are less random and more costly to

the rebel forces (Bueno de Mesquita, 2013; Wright, 2016). Additional resources might also

allow rebels to gather precise information about defensive weaknesses, including when troops

and military installations are vulnerable to attack.

In our model of irregular warfare, rebels gather information about vulnerability of the

targets and conduct attacks based to this information. As government defensive resources

are scarce as well, information about the presence of protection at one point in time is simul-

taneously information about (the absence of) protection during other periods of the day.1

1For example, following the Afghan surge in 2010, insurgents in Uruzgan province were able to monitorand assess weaknesses at one of the Coalition’s forward operating bases. Rebels had amassed an arsenal ofrockets, which they deployed strategically at particular times during the day. Despite rapid responses and a

1

With higher quality information, rebels concentrate their attacks during time periods when

targets are unprotected. This suggests a simple theoretical mechanism linking rebel capacity

and patterns of attack timing. Positive economic shocks enable rebels to acquire relatively

high quality intelligence and their attacks become clustered in particular windows of time,

i.e., exhibit low entropy. Empirically assessing the theoretical model requires unusually rich

data on when attacks occur as well as largely unobservable details about rebel spy operations.

We use newly declassified military records provided by the United States government, which

document hundreds of thousands of combat engagements in Afghanistan during Operation

Enduring Freedom, including 28,617 instances of indirect fire attacks (typically, rocket or

mortar fire). The data include within-day timestamps, often to the minute, which we col-

lapse to the hour. This allows us to study temporal clustering in attack patterns, consistent

with a deviation from random attack timing. We quantify the randomness of combat timing

by developing an extension of bootstrapping methods in statistics applied to the canonical

Kolmogorov-Smirnov test (Abadie, 2002).2 We then study the association between attack

clustering and rebel capacity using granular data on opium revenue (Peters, 2009).

We find consistent evidence that positive shocks to rebel capacity decrease randomness

in the timing of violent attacks. As predicted by the model, rebel attacks become clustered

during particular time windows following opium windfalls. In other words, insurgents begin

to concentrate their combat operations during specific periods of the day as they accumulate

resources (Table 1). This finding survives a battery of robustness checks, including when we

account for trends in violence during the fighting, harvest, and planting seasons, implement

alternative fixed effects approaches, account for regional variation in crop yield and farmgate

prices, exclude late-harvesting districts, a numerous alternative specifications of the outcome

variable and introduce a number of alternative measures of state capacity such as close air

support missions, bomb neutralization, counterinsurgent surveillance activity, and safe house

raids (Tables 2, 3, A-3, A-4). The rich nature of our conflict microdata allow us to rule out

other potential identification concerns, including rarely documented coercive tactics used by

insurgents which may influence opium production (Table A-5). Spatial correlation-corrected

randomization inference and coefficient stability tests confirm these benchmark results as

well (Figure 6, Table A-6).

technological advantage, Coalition forces were unable to neutralize the insurgent threat and carefully timedattacks continued during the subsequent fighting season. See “Despite drones and blimps, rocket attacksin Afghanistan prove hard to stop”, The Christian Science Monitor, 8/21/2012, https://tinyurl.com/

y8e5x466.2In Appendix A2.2, we discuss and implement a preliminary test of spatial clustering and find evidence

consistent with our theoretical model and main results regarding attack timing.

2

We also introduce results from a novel set of instrumental variables approaches. These

approaches employ non-parametric estimation and machine learning techniques to identify

agronomic factors which reliably predict opium productivity. Our IV approach flexibly lever-

ages daily data on precipitation and temperature fluctuation by district as well as soil quality

characteristics. These factors allow us to study variation in opium revenue that is driven by

factors outside of combatant control and, because we use only weather conditions during the

growing season months before fighting actually occurs, we sidestep potential concerns about

violations of the exclusion restriction (Tables 4, 5, 6). We use supplemental data on pre-

invasion irrigation networks, newly released data on military reconstruction projects, and

sample randomization tests to rule out other potential concerns about instrument validity

(Tables A-12, A-16, Figure 7). Overall, our IV results yield strong evidence consistent with

our main result: positive revenue shocks lead to more temporal clustering in rebel attack

patterns.

The model emphasizes the critical role of the quality of information that insurgents gather

about troop and facility weakness. As insurgents gather enough sufficiently precise infor-

mation about target vulnerabilities, their attack patterns shift as they optimally calibrate

the timing of their attacks. Our military records include previously unreleased information

about rebel spy operations—surveillance of troop movement and base activity—observed by

military forces. Our data suggests that insurgents were able to conduct surveillance oper-

ations in 70 of Afghanistan’s 398 districts in 2006 (see Figure 1). These records enable us

to test whether the ability to surveil, breach, or infiltrate targets significantly enhances the

overall impact of revenue shocks in a manner consistent with our theoretical model. Ulti-

mately, we find strong evidence that the baseline effect we observe is substantially greater

in areas where the Taliban have the capability to acquire actionable intelligence about when

troops, convoys, and bases are susceptible to attack (Tables 8, A-24, A-25). Additional data

on rebel battlefield casualties and government-led surveillance operations allow us to assess

the impact of policy interventions relevant to our theoretical model. We find robust evidence

that labor scarcity (due to battlefield losses) and increasing costs of attack clustering (due to

government surveillance) lead rebels to randomize the timing of their attacks more, yielding

less temporal clustering (Tables 9, 10).

We next investigate the battlefield consequences of attack timing. Drawing on the well-

established psychological literature on the mental health consequences of combat exposure

(Crocq and Crocq, 2000; Andreasen, 2011; Afari et al., 2015), we investigate whether tempo-

ral clustering reduces soldier efficiency during patrol operations to ‘find and clear’ roadside

3

bombs. We find compelling evidence that temporal clustering reduces the number of suc-

cessful neutralization missions and, as a downstream consequence of this reduced efficiency,

increases the number of bomb-induced battlefield casualties (Tables 11, 12). These results

suggest the study of attack timing may be central understanding soldier health during com-

bat deployments and battlefield effectiveness.

The richness of our data finally enable us to further explore when and how economic

shocks impact the production of violence. Opportunity costs, outside options, and reser-

vation wages are central to most economic theories of political violence. Unique features

of the Afghanistan case enable us to identify areas where reservation wages grow relatively

faster due to the presence of bureaucratic corruption. To assess the extent of local adminis-

trative corruption, we rely on proprietary surveys conducted for the North Atlantic Treaty

Organization by a local Afghan firm. Consistent with the theoretical models in Berman

et al. (2011) and Dal Bo and Dal Bo (2011), our results suggest revenue shocks from opium

production have a larger impact on rebel tactics in places where reservation wages are rela-

tively lower (Table 13). Savings technologies in rebel organizations may enable insurgents to

anticipate and account for revenue volatility in their expenditures during the fighting season

after particularly profitable harvests. We find no evidence, however, that rebels engage in

consumption smoothing (Table 14).

This paper contributes to the political economy of conflict. Prior work provides com-

pelling evidence that insurgents respond strategically to local economic shocks (Dube and

Vargas, 2013; Berman et al., 2017; Vanden Eynde, 2018), form alliances during war (Konig

et al., 2017), and calibrate their use of violence against civilian populations (Condra and

Shapiro, 2012; Condra et al., 2018). Recent work also links exogenous economic shocks

to terrorism financing and recruitment activity on the dark net (Limodio, 2019). Our ev-

idence highlights how sophisticated institutions commonly associated with states and gov-

ernment forces—structured tax collection schemes, combat coordination, and surveillance

operations—influence the timing of insurgent violence.

Understanding how economic shocks and government countermeasures impact rebel tac-

tics remains an important policy issue. The United States alone has spent more than two

trillion dollars on combat operations in Afghanistan. Trebbi et al. (2017) present evidence

that government counter-IED measures may have been quickly thwarted by rebels. Our

evidence, on the other hand, suggests labor constraints and government surveillance may

meaningfully impact how rebels fight.

The rest of the paper is organized as follows. Section 2 provides a brief overview of the

4

related literature. Section 3 introduces our theoretical model. Section 4 details the empirical

strategy. Section 5 presents the main results and robustness checks. Section 6 analyzes

the potential mechanisms such as intelligence gathering by rebels and labor scarcity, while

Section 7 discusses results that relate battlefield outcomes to temporal clustering of attacks.

The short Section 8 presents additional results on IO of violence production. The final

section concludes.

2 Economics of Political Violence

Quantitative work on the economics of conflict has largely focused on the conditions that

trigger warfare. Fearon and Laitin (2003), Collier and Hoeffler (2004), Miguel, Satyanath

and Sergenti (2004), and Bazzi and Blattman (2014) study the proximate causes of conflict.

Related work explores incentives to use violence as a means to predate or capture economic

resources (Le Billon, 2001; Ross, 2004; Hidalgo et al., 2010). Others have focused on the

link between income shocks and levels of political violence at a subnational level (Dube

and Vargas, 2013; Jia, 2014; Wright, 2016; Vanden Eynde, 2018; Gehring, Langlotz and

Kienberger, 2019). A meaningful gap exists, as Berman and Matanock (2015) point out,

between our understanding of when and how rebels engage in armed combat. We advance

this agenda by examining the relationship between economic shocks to rebel capacity and

the ways in which insurgents fight.

Violence is economically and politically costly. Gould and Klor (2010) find that terror

attacks harden in-group biases and cause Israelis to adopt less accommodating political po-

sitions.3 Those affected by these attacks are also more likely to vote for right-wing parties.

Similarly, Condra et al. (2018) find that insurgent attacks around elections in Afghanistan

are calibrated to avoid civilian casualties and substantially reduce voter turnout. Violence

may be triggered by and reinforce ethnic divisions (Esteban and Ray, 2011; Esteban, Mayoral

and Ray, 2012), even in institutions designed to maintain impartiality (Shayo and Zussman,

2017). Insecurity might also undermine political instability through a realignment between

international actors and domestic power brokers (Padro i Miquel and Yared, 2012). Civil

conflict is also economically disruptive (Abadie and Gardeazabal, 2003), even at the mi-

crolevel (Besley and Mueller, 2012). Our results help us better understand how insurgents

respond to rent shocks and may enable governments to better anticipate and defend against

attacks.

3See also Berrebi and Klor (2008) and Getmansky and Zeitzoff (2014).

5

More generally, our paper provides insights into the working mechanism of insurgency.

State capacity is central to economic theories of conflict (Besley and Persson, 2011; Gennaioli

and Voth, 2015; Besley and Persson, 2010; Powell, 2013; Carter, 2015; Esteban, Morelli and

Rohner, 2015). Yet the resources available to the state’s competitors also influence when

conflicts emerge (Dube and Vargas, 2013), how internal wars are fought, and whether they

end in withdrawal. Recognizing this gap, Bueno de Mesquita (2013) theorizes that the

relative strength of the rebellion influences leaders’ choice to adopt irregular tactics. We

advance this literature by developing a microlevel theory of the relationship between resource

endowments and combat tactics.

Technology of conflict has long been an active area of theoretical modelling (Kress, 2012).

Optimal allocation of attacking and defensive resources have been studied in the Colonel

Blotto-type games starting with Borel (1921). Our game is not a “Blotto game” in the

sense of Roberson (2006), which assumes that the side that allocates more resources to one

battlefield wins for sure, yet is “Blotto” in the sense of Blackett (1958) and Powell (2007b),

which allow for the probability of success to depend on allocated resources more generally.4

A contribution of our model is the signal about the relative vulnerability of different targets

that rebels receive before launching attacks: it allows to analyze comparative statics with

respect to the quality of information.

In a setting in which the maximand is the sum of harm to individual sites, Powell (2007a)

demonstrates that in the unique equilibrium, the defender minimaxes the attacker regardless

of whether or not the attacker can observe the defender’s allocation before choosing where to

launch the attack. In Powell (2007a), the defense has private information about the relative

vulnerability of two sites, and allocated protection is public information, which creates the

secrecy vs. vulnerability trade off. Goyal and Vigier (2014) consider a zero-sum Tullock-type

conflict, in which the defense chooses a network to protect and the attacker chooses where

to launch an attack. In particular, they show that a star network with all defence resources

allocated to the central node is optimal in many circumstances. In Konig et al. (2017),

the network is given; the data on the Second Congo War is used to estimate the impact of

selective dismantling of fighting groups and weapons embargoes on conflict intensity. We

estimate the potential effects of abnormal battlefield losses (a negative shock during the

fighting season partially offsets revenue windfalls), which is close to selective dismantling in

Konig et al. (2017).

4See Golman and Page (2009), Roberson and Kvasov (2012) and Konrad and Kovenock (2009) for recentadvances and Kovenock and Roberson (2012) for an excellent survey.

6

3 Theory

The spot where we intend to fight must not

be made known; for then the enemy will

have to prepare against a possible attack at

several different points; and his forces being

thus distributed in many directions, the

numbers we shall have to face at any given

point will be proportionately few.

Sun Tzu, ibid.

In our model of temporal clustering of attacks, a rebel group chooses the number of

attacks using information it gathered about the targets’ vulnerability. This is a Colonel

Blotto-type model with asymmetric information that yields empirical implications that can

be directly test using our empirical approach. This approach utilizes randomization inference

and the bootstrap Kolmogorov-Smirnov method developed by Abadie (2002).

3.1 Setup

Consider a rebel group that attacks the government facilities using a certain technology

(e.g., mortars). The group uses information of the quality θ ∈[

12, 1]

to allocate the total of

a attacks across different targets (time slots). The government allocates resources to defeat

attacks.

There are n time slots to protect.5 The government has resources to defend r < n time

slots. Formally, the government strategy is a probability distribution G (·) over n-tuples

(g1, ..., gn) such that∑

i∈n gi = r and gi ∈ {0, 1} for each i ∈ n. If an attack happens during

the period when the target is defended, it does not succeed; if an attack is in an unprotected

time slot, it succeeds with probability p ∈ (0, 1) . Since any deterministic choice of protec-

tion will result in rebels attacking outside of the time slots when the targets is defended,

any reasonable placement of protection should be randomized. After the government allo-

cates protection, rebels gather intelligence about the targets’ vulnerability during different

5We consider targets to be “time slots” rather than space objects as this corresponds with our empiricaldata. Therefore, it is natural for rebels to maximize the probability of at least one successful attack, ratherthan the expected number of destroyed targets, which would be natural if targets were space objects. Ourformal results extend to this alternative setting as well. In Appendix A2.2, we introduce and implement apreliminary solution to the spatial clustering counterfactual problem (described in detail in Subsection 4.4).Our results are consistent with increased spatial clustering as rebel capacity increases.

7

time-periods. Specifically, rebels receive noisy signals (si)i∈n ∈ {0, 1}n that are determined

according to

P (si = 0|gi = 0) = P (si = 1|gi = 1) = θ.

Then the rebels strategy is a mapping F (a1, ..., an; ·) from the n-tuples of signals about peri-

ods’ vulnerability into a probability distribution on n-tuples (a1, ..., an) such that∑

i∈n ai = a

and ai is a non-negative integer for each i ∈ n.

The rebel group maximizes the probability of at least one successful attack net of the

cost of attacks and information gathering. As gathering intelligence requires resources, we

assume that the quality of information θ is a function of revenues in rebels’ disposal. 6 Thus,

the periods of low rents correspond to both lower quality of information available to rebels

and lower number of attacks that the rebel group can potentially launch. The government

is interested in minimizing the probability of at least one successful attack.

The game starts with the government allocating its defensive resources across n time slots.

Then rebels receive noisy information (si)i∈n ∈ {1, 0}n about the government’s defense and

choose the distribution of their attacks across the slots.

Definition 1 Given the resources available to rebels, an equilibrium is rebels’ choice of a

c.d.f. F ∗(s1, ..., sn; ·), which is a function of signals about each time slot, into a probability

distribution over a attacks on each of the n time slots, and the government’s choice of a

c.d.f. G∗ over r−combinations of n time slots. Given G∗, F ∗ maximizes the probability of

at least one successful attack net of the cost of attacks and information gathering; given F ∗,

G∗ minimizes it.

3.2 The Attack Timing Game

We start backwards. It is straightforward to establish that the government allocates resources

into r time slots chosen randomly and uniformly across all possible combinations. The rebels’

optimal strategy depends on the signals that they observe. Information gathering results in

x “vulnerable” (si = 0) and n−x “defended” (si = 1) time slots. The rebel’s assessment that

a particular time slot i is vulnerable is based on two pieces of information: first, the signal

about its vulnerability, si, and the total number of “vulnerable” signals, x = {j|sj = 0},which is a random variable, the sum of two random variables with binomial distributions

6In earlier version of the argument (available upon request), we explicitly model the allocation of resourcesbetween additional number of attacks and information precision, taking into account the marginal costs ofthese activities.

8

with different probabilities of success: n − r vulnerable time slots produce signal 0 with

probability θ, while r defended time slots produce signal 0 with probability 1− θ.7

Intuitively, when resources are scarce, a signal about vulnerability of one period is in-

formative about the vulnerability of other periods, even though signals are conditionally

independent. Indeed, if one time slot is more likely to be vulnerable, other time slots are

less likely to be vulnerable as probability of being one of r − 1 protected time slots among

n − 1 periods is smaller than to be one of r among n. The number of “vulnerable” signals

x is not necessarily equal to the total number of attacks a; in fact, x can be any integer

between 0 and n with a non-zero probability. In the two extreme cases, x = 0 (there are no

time slots that are signaled to be vulnerable) and x = n (all potential times an attack could

occur are signalled to be vulnerable), there is no information to update upon. In all other

cases, 1 ≤ x ≤ n− 1, signals are informative:

P (gi = 0|si = 0) > P (gi = 0|si = 1).

The rebels’ optimal strategy is a function of the probability that a given time period that

is signaled to be vulnerable is indeed vulnerable,

q(x) = P (gi = 0|si = 0,#{j|sj = 0} = x).

Consider the rebels’ choice of one attack across two time slots with conditional (on x) prob-

abilities of being vulnerable q1 and q2, respectively, with q1 > q2. If there are no attacks

already planned on during these times, then an attack timed during the first period provides

a higher marginal probability of success (see also Powell, 2007b). At the same time, the fact

that the vulnerable time slot has a higher probability of success does not mean that all at-

tacks should be concentrated during times when the target is vulnerable. Suppose that there

are already m attacks planned during the first time period, m ≥ 1, and no attacks planned

on the second time slot. One more attack during the first time slot results in q1 (1− p)m of

marginal probability of success as with probability 1−(1− p)m one of the m attacks that are

already planned succeeds. An attack that occurs during the second time window contributes

q2p. Thus, given some sufficient capacity, it is optimal to launch some attacks during the

second, less likely to be vulnerable, period.

The important role in determining the optimal strategy is played by the critical ratio

7The probability distribution of a sum of two or more binomial random variables, i.e. sums of independentBernoulli trials, with different success probabilities is sometimes called Poisson binomial distribution (Hillionand Johnson, 2017).

9

ρn,r(x|θ) of the probability that the time slot is vulnerable to the probability that the time

slot is defended, both probabilities conditional on the total number of “vulnerable” signals

x. As the detailed calculations in Appendix A demonstrate, this ratio can be derived using

the following recursive formula:

ρn,r(x|θ) =n− x+ 1 + (x− 1)ρn−1,r(x− 1|θ)

n−xρn−1,r(x|θ) + x

for 1 ≤ r, x ≤ n− 1,

with the recursion on both total number of slots, n, and the total number of “vulnerable”

signals received, x. Using the critical ratio ρn,r(x|θ), one can demonstrate that the optimal

strategy always requires allocating the first (random) attacks against the slots with “vul-

nerable” signals until the threshold dn,r(x|θ) = mini≥1

{i|ρn,r(x|θ) (1− p)i < 1

}is reached,

the next attacks against slots with “defended” signals, then against the “vulnerable” slots

again, etc. Proposition 1 summarizes the above intuition.

Proposition 1 There exists a unique equilibrium in the attack timing game. The govern-

ment protects r time slots chosen randomly and uniformly across all possible combinations

and rebels follow the signals that they receive. For any number x of slots that are “vulnerable”

(have si = 0), there is an optimal number of attacks a(x) such that min {a, xa(x)} attacks

are distributed uniformly over x “vulnerable” time slots. The remaining a −min {a, xa(x)}attacks are distributed uniformly across n− x “defended”slots.

The term min {a, xa(x)} appears in the statement of Proposition 1 because it is possible

that the threshold a(x) is such that xa(x), the desired number of attacks during vulnerable

time slots, might exceed the capacity a. For example, if n = 5, a = 3, and intelligence about

defensive weaknesses suggests two specific time windows are likely to be vulnerable, the

optimal strategy might call for a(2) = 2, i.e. two attacks should be launched during each of

the two vulnerable time slots. With the capacity of launching only three attacks, the rebels

would have to choose the period for the double attack randomly over the two vulnerable

time windows.

3.3 The Rebel’s Demand for Precise Information

The rebels’ equilibrium strategy described in Proposition 1 depends on the quality of in-

formation θ. A higher precision of information leads to a higher temporal concentration of

attacks: more attacks are launched during time periods that intelligence gathering indicated

as “vulnerable”. For any number of “vulnerable” signals x, the optimal strategy requires to

10

launch (weakly) more attacks during the vulnerable time windows. This, in turn, leads to a

decrease in the natural measure of randomness of attacks, the entropy∑n

i=1aia

ln aia, which

is maximized when attacks are distributed uniformly across time intervals.

Proposition 2 For any amount of rebels’ resources, the higher is the precision of informa-

tion that rebels receive, θ, the higher is the temporal clustering (concentration) of attacks,

i.e., the lower is the expected number of unique periods attacked and the larger is the expected

number of attacks (both successful and total) per time slot attacked.

The critical element of Proposition 2 is that for any number x of time slots that are

signaled to be vulnerable after the information is collected, the probability q(x) that a

time window marked vulnerable is indeed vulnerable is (weakly) increasing in the precision

of information θ, and thus the threshold a(x) is (weakly) increasing in θ for any x. As

a consequence, more precise information leads to a higher concentration of attacks: more

attacks are launched during a smaller number of time slots. In the extreme case of perfect

information (θ = 1), attacks are uniformly randomized over all n− r vulnerable time slots.

In the opposite extreme, when the signals are completely uninformative (θ = 12), all time

windows are equally likely to be vulnerable. In this case, the optimal strategy for rebels is

to launch a attacks chosen randomly and uniformly across all time slots.

In equilibrium, the optimal choice of rebels depends, in addition to precision of informa-

tion θ, which in turn is a function of the rebels’ resources, on the number of potential time

slots for attacks n, the resources in the disposal of the government r, and the efficiency of

weapons p. Proposition 2 establishes that a lower precision of information, a result of a fall

in revenues, leads to attacks becoming less temporally concentrated; a decrease in the total

number of attacks due to a fall in resources would not affect temporal concentration. This

increase in entropy as a result of decrease in resources is the central empirical implication

of our model which is tested, using the technique suggested in Abadie (2002), in Sections

4-5. (See Subsection 4.4 for the methodology of detecting temporal patterns of combat.)

Proposition 3 formally states the comparative statics results with respect to the govern-

ment’s resources and efficiency of rebels’ weapons, which we evaluate empirically in Section

6.

Proposition 3 More resources in the government’s disposal (a higher r) and less efficient

weapons, i.e., a lower p, result in a higher temporal concentration of attacks (lower entropy).

Proposition 3 states that an increase in government resources has the same effect as a

fall in rebels’ resources, but the mechanism is slightly different. A higher r, the amount of

11

protection at the government disposal, decreases the probability of rebels’ success as the ex

ante probability that each time window is protected increases. This has the same effect as

the fall in rebels’ revenues, which results in less information gathering and, therefore, less

temporally concentrated attacks.

The theoretical model can be extended in a number of ways. At the expense of much

cumbersome algebra, it is possible to incorporate the trade off between an increase in the

number of attacks and an increase in the precision of intelligence gathering as a result of

an increase in rebels’ resources. For our purposes, it is sufficient that an increase in rebels’

resources cannot lead to a decrease in the quality of information. It is also possible, perhaps

more realistically, to model a dynamic, rather than a one-shot interaction between the gov-

ernment and rebels. Given that our own estimates demonstrate the very limited ability of

rebels to smooth the availability of their resources over fighting seasons (see Subsection 8.2

and Table 14), we leave the dynamic extension for future papers.

4 Empirical Design

In this section, we discuss the setting of our investigation, review our microdata, and intro-

duce our identification strategy.

4.1 Context

We study the relationship between combat activity and rebel capacity in Afghanistan. We

focus specifically on the well-documented link between opium production and Taliban tax

extraction. In the primary opium producing regions, seeds are planted in late fall and early

winter. The growing season ranges from February through April, with most opium latex

harvested and packaged in May and June. Taliban commanders and veteran fighters return

from Pakistan in June to collect taxes from opium farmers (ushr, typically a flat 10% fee

mandated by the Quran).8 Taxes can be paid in currency, opium blocks, or other goods, such

as motorcycles, offroad vehicles, and weaponry. The Taliban also benefits from protection

fees levied on opium traffickers as they pass through rebel-held territories.9

8For a detailed account of the industrial organization of the Taliban, see Peters (2009).9It is worth noting, as highlighted by Mansfield (2016), taxation by the Taliban is not perfectly uniform.

In areas where the Taliban are not sufficiently powerful, the amount collected may be reduced (reflecting alocal-level bargain with tribal leaders). Microlevel data on tax collection does not exist. Given the approachwe detail later, we anticipate that this concern would bias our estimated effects downward. In Table A-7,we use historical territorial control (from the height of the Taliban) to evaluate this conjecture. Indeed, we

12

Taxes are collected by fighters and receipts are distributed to farmers to prevent double

taxation. Fighters pass their collections to district-level commanders (equivalent in scale to

US counties). Taxes are subsequently passed upward to provincial and regional comman-

ders, who keep ledgers of their annual revenue and are subject to audit by the Taliban’s

Central Finance Committee, based out of southwestern Pakistan. Most proceeds remain

with the district commander, for conducting operations in the subsequent fighting season

which typically lasts until September. These funds can be used to purchase weapons and

ammunition, as well as covering the salaries of fighters and rebel informants. The Central

Finance Committee (CFC) retains the authority to demote or relocate field commanders

to less desirable fronts if audit irregularities are found. The remaining revenue is split be-

tween supporting operations conducted in resource-poor districts where local taxes alone are

insufficient for supporting rebel attacks and developing Taliban infrastructure in Pakistan

(including small-scale hospitals for wounded fighters).10

We focus primarily on the period from 2006 to 2014. The industrial organization of the

insurgency, most notably the taxation and command structures oriented around administra-

tive districts, emerged in 2006. These institutions are central to our argument that revenue

influences combat tactics. Our military records track insurgent operations until the end of

2014, when the NATO Operation Enduring Freedom was transitioned to Mission Resolute

Support.

4.2 Conflict Microdata

Our investigation exploits newly declassified military records which catalogue combat engage-

ments and counterinsurgent operations during Operation Enduring Freedom in Afghanistan.

These data were maintained by and retrieved through proper declassification channels from

the U.S. Department of Defense. The data platform was populated using highly detailed

combat reports logged by NATO-affiliated troops as well as host nation forces (Afghan mili-

tary and police forces). Data of this type differ substantially in coverage and precision from

media-based collection efforts (Weidmann, 2016). As Weidmann (2016) points out, these

tactical reports represent the most complete record of the war in Afghanistan. Additional

find that our main effect is attenuated downward in places the Taliban could not have taxed fully prior tothe US-led invasion.

10We observe variation in the opium tax base of each district, not receipts from the CFC. This type ofredistribution will bias our point estimates towards zero.

13

details on data collection are discussed in Shaver and Wright (2017).11

The detailed nature of our conflict microdata allows us to track insurgent activity by

the hour. Although this data tracks dozens of types of violence, the majority of enemy

action events are characterized as indirect fire, direct fire, and IED explosions. Indirect

fire consists of mortars and other weapons that can be deployed without close contact with

military forces. Direct fire attacks are primarily line-of-sight, close combat events. IEDs

consist of explosives that have been emplaced and are detonated through a variety of trigger

mechanisms (pressure plate, cable-to-battery, radio signal, laser beam, etc.). Subsets of these

data are also studied in Callen et al. (2014), Beath, Christia and Enikolopov (2013), and

Condra et al. (2018), and are highly comparable to tactical data collected in Iraq (Berman

et al., 2011).12

Our military records include information about counterinsurgent operations, including

find and clear missions that neutralized emplaced IEDs, discoveries of weapon caches, such

as small arms, ammunition, and bomb making materials, and provision of close air support,

which was used primarily to harden mobile targets and extract coalition forces that were

pinned down at a fixed location by insurgents. We supplement this information with mea-

sures of insurgent capture and detention, counterinsurgent surveillance operations, and safe

house raids yielding actionable intelligence about rebel operations. This information enables

to address operational factors that may confound the relationship we are trying to estimate.

In particular, it might be the case that counterinsurgents strategically assign additional

fighting capacity to districts with a substantial rebel presence and where opium production

is high. Shifts in government resources, like the ability to identify and neutralize weapon

caches or to use aerial bombardment to assist troops engaged by insurgents, might also in-

fluence the temporal patterns of insurgent attacks. These operations also lead to battlefield

losses for insurgents (in the form of fighter casualties), which we utilize to study the impact

11These data are similar to the War Logs released by WikiLeaks in 2010. The most important differencesare that the data we study here are more complete (2009 versus 2014) and have been formally declassified.

12It is important to note that insurgents have differential control over the exact timing of each of thesetypes of combat. Indirect fire events can be initiated at any time against stationary targets. For example,a large number of mortar fire attacks were launched from hillsides and targeted military outposts. As such,insurgents maintained a high level of control over when these events occurred. Direct fire attacks are typicallyfrontal assaults on convoys or forward deployed troops conducting combing operations in remote villages.Although insurgents decide if to attack, conditional on having the opportunity, the timing of these attacks ispartially determined by the movement of troops, the timing of which may be determined by a non-stochasticprocess. Similarly, roadside bombs may be planted hours or days before they are triggered. Some of thesebombs may also be detonated by unintended targets, which further reduces insurgent control over the timingof these attacks. For these reasons, we focus our main analysis exclusively on the timing of indirect fireattacks. We discuss this in more detail in the Appendix A2.7.

14

of labor scarcity on combat tactics.

Opium production may be influenced by combat operations and more direct attempts by

insurgents to coerce the local population (Lind, Moene and Willumsen, 2014). In particular,

insurgents may use violent and non-violent tactics to intimidate civilians, such as killings

of government collaborators and the posting of ‘night letters’ and other non-lethal shows

of force. Fortunately, our military records include information about these tactics as well,

enabling us to address potential concerns about residual endogeneity in estimated levels of

opium production.

Another unique feature of our conflict data is information on rebel surveillance operations,

military installation breaches, and insider attacks. Enemy surveillance operations are logged

whenever security forces become aware of attempts by insurgents to track troop and vehicle

movement and day-to-day activities on military bases. This kind of insurgent spy activity

can be, and likely is, used to identify troop and infrastructure vulnerabilities. We illustrate

the location of these spy operations in Figure 1. In addition to surveying force activity

from outside of military compounds, insurgents can infiltrate these installations and monitor

activity from within. These security breaches might also result in direct confrontations

between insurgent and counterinsurgent forces. Records of insider attacks also reveal Taliban

attempts to ‘turn’ Afghan security forces, and launch deadly attacks from within operational

units. We use these unique pieces of information to more explicitly test the observable

implications of our model regarding intelligence gathering and the quality (precision) of

information about government vulnerabilities.

4.3 Opium Cultivation and Prices

We supplement our military records with data on opium production and prices. Opium

production estimates are derived from ground-validated remote sensing techniques, which

use high resolution satellite imagery to track changes in vegetation during the spring har-

vest. UNODC-Afghanistan randomly spatially samples potential agricultural zones within

provinces and acquires pre-harvest and post-harvest imagery (see Figure 2, panel (a)). These

images are then examined for changes in vegetative signatures consistent with the volatile

wetness of opium plants after lancing. From this sampling technique, officers estimate the

spatial risk of opium production. This enables them to calculate granular estimates of opium

production (see Figure 2, panel (b)). These gridded estimates are then compiled as the an-

nual amount of opium production (in hectares) for each district. We correct for changes in

the administrative boundaries of districts over time using the Empirical Studies of Conflict

15

(ESOC) administrative shapefile. To translate production into yields, we compile additional

details about annual yield (kilograms per hectare) from UNODC-Afghanistan annual reports.

These figures are available at the national level as well as by region.

Opium price data is compiled at national and regional levels. These prices are tracked

monthly at various locations across the country via a farmer and market spot price survey

system. In Figure 3, panel (a), we introduce the monthly time series for the two price-

making regions, Kandahar and Nangahar. Our main specification utilizes the simple average

between these prices in June, when taxes are collected (vertical lines added for clarity). In

supplemental results, we study the regional price time series in Figure 3, panel (b). We rely

on UNODC-Afghanistan documentation to assign districts to price zones. We extract exact

prices using WebPlotDigitzer software.

4.4 Detecting Temporal Patterns of Combat

We now introduce a method for detecting temporal clustering of attack patterns. We focus

on timing rather than spatial allocation of attacks due to the tractability of estimation.

Most importantly, while we know time windows when attacks do not occur, it is much

more difficult to identify counterfactual targets that were not attacked since there exists

no publicly available comprehensive data on the spatial allocation of military assets across

time (e.g., bases, patrol movement, unmanned infrastructure).13 Given the importance of

counterfactuals to our measurement strategy, we focus primarily on temporal clustering.

Our approach to quantifying patterns of combat timing employs randomization inference

and the bootstrap Kolmogorov-Smirnov method developed by Abadie (2002). The central

intuition of this approach is to use randomization inference to better understand the degree

of temporal clustering we observe in insurgent combat operations (by hour). The method is

executed in several steps.

1. Fit a local polynomial regression to the observed distribution of violence by hour. We

specify a conservative bandwidth of 1. This empirical distribution of fitted values is

stored.14

13In Appendix A2.2, we introduce a preliminary solution to the spatial counterfactual problem. Weimplement this solution, calculate a spatial dispersion parameter, and find robust evidence that spatialclustering increases with revenue (see Table A-2).

14Some conflict events lack a time stamp (∼3%). Because we cannot assign these events an hour, they areexcluded from the calculation of the empirical distribution.

16

2. Identify the sequence of district-hours during which indirect fire engagements occur.

For each district-hour, we know the sum of the number of attacks.

3. Randomly shuffle the sequence above. This is equivalent to a randomization or per-

mutation test.

4. Fit a local polynomial regression to the randomly shuffled distribution of violence by

hour. The simulated distribution of fitted values is stored.

5. Execute the bootstrap Kolmogorov-Smirnov test. This test is composed of four ele-

ments.

(a) Compute the TKSdfi for the fitted values of the empirical and simulated distribu-

tions, where:

TKSdfi =

(n1n0

n

) 12

supy∈R∣∣F1,n1(y)− F0,n1(y)

∣∣.(b) Resample observations with replacement from observed and simulated distribu-

tions. Split the resampled set into two distributions and calculate TKSdfi,b. Store

TKSdfi,b.

(c) Repeat prior two steps 1,000 times.

(d) Calculate and store the likelihood parameter of the tests as∑1000

b=1

1{TKSdfi,b>T

KSdfi }

1,000,

where the numerator is an indicator function.

6. Repeat steps 2 through 5 10,000 times. Evaluate the central tendency (mean) of the

likelihood parameters.

7. Replace zero values with the minimum observed non-zero rank value and calculate the

log.

To clarify, we identify the hour of each attack within a given district-year (fighting season).

We then reshuffle the hour vector and compare the empirical distribution to the randomly

reshuffled vector. This process is repeated many times per district-year. The result of

the technique is a single likelihood parameter, which we call a p-value, for each unit of

observation. We estimate these parameters for district-years with a minimum of five conflict

events.15 Higher p-values indicate that the distribution of rebel attacks by hour cannot be

15We set the lower threshold at five events to ensure convergence of the simulations. A conflict vector thatis too short (i.e., fewer than five) does not permit sufficient randomization when the hour vector is reshuffled.Our results are highly consistent if we raise this threshold upward.

17

distinguished from randomness. Lower p-values reveal attack patterns that are more easily

differentiated from randomness; i.e., they are more predictable.

It is important to note here that this parameter does not clarify what exact time windows

experience differential attack intensity. One benefit of our approach is that we do not need to

make additional assumptions about potential temporal weaknesses of military installations

across seasons in the same district or across districts in the same season (e.g., dawn or dusk

hours). Instead, the parameter flexibly captures a uniform measure of temporal clustering

even when the underlying distributions differ across locations or periods.

Estimation of our likelihood parameters using this technique requires tens of billions

of simulations, so we use several supercomputers. In Figure 4, we plot the calculated p-

value (log) distribution for indirect fire attacks. Most district-year p-values above -10. This

distribution is characterized by a long left-side tail. This suggests that specific district-

fighting seasons exhibit very clear evidence of temporal clustering (i.e., non-randomness).

4.5 Empirical Strategy

We study the relationship between rebel capacity and randomized combat by examining

whether the within-day distribution of violence for each district’s fighting season is associated

with rent extraction from opium. If the results follow our expectations, rebel capacity and

the likelihood parameter of our simulation test above should be negatively correlated.

To test the relationship between randomization of attack timing and insurgent capacity,

we estimate the following ordinary least squares regression:

log(pvald,y) = α + β1log(productiond,y + 1)× log(pricey) + Fy + ΛXVd,y + ε (1)

Where pvald,y is the p-value for a given district, d, and fighting season, y (year). Fy cap-

tures fighting season fixed effects (equivalent of year in the study sample) and XVd,y captures

a vector of additional covariates, which we incorporate to address potential concerns about

omitted variables. These covariates include the intensive margin of insurgent operations

during the fighting, harvest, and planting seasons as well as supplemental measures of state

capacity and insurgent intimidation and alternative fixed effects specifications. We expect

the first coefficient β1 to be negative.

18

5 Results

We begin by visualizing the data. In Figure 5, we plot the p-value distributions for indirect

fire attacks against the corresponding opium revenue of each district-year (fighting season).

Confidence regions (95%) are shaded in blue. Notice the consistently negative relationship

between revenue and randomness of combat. This non-parametric correlation is consistent

with our intuition that high capacity rebels produce patterns of violence that are less random

and exhibit temporal clustering.

5.1 Baseline Results

We next turn to our regression-based evidence. In Table 1, we estimate Equation 1. Column

1 is a sparse model that demeans our bivariate correlation by fighting season. We find that

a strong negative relationship between opium revenue and combat randomness, confirming

our visual evidence. In Columns 2 through 4 we sequentially add controls for the intensive

margin of fighting during the fighting, harvest, and planting seasons respectively. We do this

to address potential concerns that our bivariate result is driven by a strong relationship be-

tween opium revenue and the intensity of violence during the fighting season (which covaries

negatively with our randomness parameter). Wright (2016) finds evidence of this type of

positive level shift in violence in Colombia.16 It is also possible that there is a mechanical

correlation between the intensity of combat activity and the test statistic if, for example,

it is easier to detect clustering in the presence of a large number of events. Accounting for

these channels leaves our results are largely unaffected, although our point estimate becomes

marginally more precise in Column 2. In Column 3, we attempt to rule out concerns that

our estimates are substantially biased by the endogenous relationship between opium pro-

duction and insurgent violence during the harvest season, which might influence subsequent

conflict during the later fighting months (Lind, Moene and Willumsen, 2014). It might also

be the case that farmers are coerced into planting opium through violence exposure. We

account for this potential source of bias by including a planting season violence trend in

Column 4. This baseline evidence suggests a precise, consistent link between rebel capacity

16Theoretically, it is also possible that revenue shocks via the opium channel increase opportunity costs,which would cause a level reduction in violence. Gehring, Langlotz and Kienberger (2019) present evidenceconsistent with this pattern, though the authors focus on violence in the subsequent calendar year rather thanthe fighting season that immediately follows post-harvest tax collection. We repeat this analysis, focusingon the fighting season, and find a large positive reduced form (Table A-8) and second stage result (TableA-9).

19

and randomization of indirect fire attacks.

Robustness Checks We conduct several other baseline robustness checks in Table 2. Col-

umn 1 replicates the fully saturated model from Table 1. In Column 2, we introduce a

province × fighting season fixed effect, which soaks up any residual mechanism design ef-

fects due the spatial sampling procedure utilized by the UNODC to estimate local opium

production. This fixed effect also absorbs troop rotation schedules which coincide with the

province-year, which includes force movement into and out of regional command posts. Al-

though the magnitude and precision of our main effect declines marginally, the negative

relationship persists even in this very demanding specification. Another potential concern

one might have is that the strategy we use to account for the intensive margin of violence

during the fighting season (i.e., partialling out the violence in levels) is incomplete. Another

solution is to inversely weight our model along this margin. This implies that our corre-

sponding estimate is less vulnerable to vertical (conflict) outliers. We present this result in

Column 3, which is highly consistent with our baseline result.

In our baseline specification, we rely on a national time series in prices and year-by-year

variation in opium yields (kilograms per hectare). Yet the interaction of weather conditions

and soil suitability may lead to heterogeneous crop yields by region and year. Regional prices

might also differ substantially. These two concerns represent classical error-in-variables,

which we can correct with regional price and yield data compiled from UNODC records.

In Column 4, we replicate our baseline specification in Column 1 using opium revenues

calculated using regional yield rates and regional price data. It is also the case that some

provinces have later harvests which occur after fighting has begun in other parts of the

country. In Column 5, we use crop calendar maps produced by the UNODC to classify late

harvest districts and exclude them from our sample in Column 1. Again, our results are

highly consistent in both model specifications. In Column 6, we add a district fixed effect,

to absorb in time-invariant district-specific unobservable characteristics that may influence

opium production and combat tactics. In the main specification, we omit unit fixed effects

because our main analysis is an unbalanced panel. Because of this structure our estimating

sample is slightly reduced because we exclude singletons from the analysis. The main effect

remains substantively large and precise.

Another potential concern regards the ease of interpreting our outcome of interest (the

p-value of the randomization test outlined above). If, much like standard research practice,

we set thresholds for classifying precision, we can produce a set of more easily interpretable

outcomes (where p-values at or below a threshold indicate clustering and no clustering other-

20

wise).17 Although we prefer the continuous measure as it leverages all available information

from the continuous parameter, we produce a set of results using various thresholds from the

data (.05, 01, .002 (the median), .001, and .0005). Since the binary variable turning ‘on’ indi-

cates evidence of clustering at or below the threshold, the coefficient should flip and become

positive (revenue is positively correlated with the binary indicator of clustering). These

results are presented in Table 3. Across these various thresholds the results are robustly

positive and once we focus on thresholds at or below .01, the magnitudes are comparable

in scale. At the median (Column 3), these results suggest that a one standard deviation

increase in opium revenue increases the probability of temporal clustering of attacks by .125.

In Figure 6, we address potential concerns about spatial correlation in opium production.

To do this, we introduce two spatial correlation-adjusted randomization inference tests, where

randomization is stratified by province (A) and district (B). In each case, values are randomly

drawn within each spatial strata across years and strata fixed effects are added to the model

specification. Again, our benchmark effect is in the tail of each zero-centered distribution,

suggesting that our main effects are unlikely to have occurred by random chance even in the

presence of spatial correlation.

Additional Potential Threats to Identification In the online appendix, we address

several other potential threats to identification. First, in Tables A-3 and A-4, we address

potential concerns that the accumulation of rebel capacity which is observable to counterin-

surgents may induce a strategic response during the subsequent fighting season. Heterogene-

ity in counterinsurgent investments correlated with our measure of revenue may complicate

estimation. In principle, these factors may be bad controls due to their simultaneous or post

treatment allocation. Nonetheless, we confirm that our results remain robust if we account

for six measures of counterinsurgent capacity: close air support missions, cache discoveries,

IED neutralizations, detention of insurgent forces, counterinsurgent surveillance operations,

and safe house raids yielding actionable intelligence assets (salary and recruitment logs, hard

drives, forensic materials, etc.).18 Second, opium production might also be influenced by co-

ercive tactics used by the Taliban to intimidate civilians. This is problematic for estimation

if coercion and combat tactics are correlated. In typical settings, these coercive tactics are

unobserved or unrecorded. In our context, the military records we study track attempts to

17We thank Juan Vargas for this suggestion.18Another potentially relevant type of state capacity is opium eradication. Although government in-

vestments in eradication vary across years, UNODC reports suggest that verified opium eradication reducesnational output by roughly 1 to 3% annually. Due to the small scale of these operations, we do not anticipateeradication meaningfully impacts Taliban revenue or tactics.

21

intimidate the civilian population, using methods like ‘night letters’ and shows of non-lethal

force as well as deliberate killings of government collaborators (like informants and secu-

rity force recruits). We present these results in Table A-5, which confirm the robustness of

our main results.19 Finally, to evaluate the cultivation component of revenue, we add one

hectare to non-producing districts before we evaluate the logarithm. It is possible that our

core results are sensitive to this choice. Relatedly, districts that do not produce opium (zero

revenue) may have an outsize influence on our estimated effects and statistical precision. We

rule out these concerns in Tables A-10 and A-11, where we first exclude non-producing dis-

tricts from our estimating sample and, conditional on excluding non-producers, replicate the

Table 1 without adding a hectare.20 The estimated effect of opium revenue once we exclude

non-producers and/or adjust the measure of cultivation is larger than the main estimate

and remains statistically precise. These results suggest our core estimates are unlikely to be

driven by measurement of revenue or inclusion of district-years where no opium production

takes place.

5.2 Instrumental Variables Approach

We next introduce an instrumental variables approach. We begin by estimating opium suit-

ability using a combination of degree-day, precipitation-day, and soil quality characteristics.

This approach treats production across the full district-year panel of available data as an

outcome of interest and uses these agronomic characteristics to produce fitted values of ex-

pected productivity given observed district-year input availability. We then standardize these

predictions based on exogenous agronomic conditions and weight these values by aggregate

production in the prior year, which is correlated with present year prices.

5.2.1 Agronomic Suitability for Opium Production

We leverage data high resolution data on temperature, rainfall, and soil quality to construct

a measure of opium suitability.

We gather daily, district-level temperature (Kelvin) and precipitation (mm) measures

19In the online appendix, we present results from a Oster (2017) coefficient stability test, using the addi-tional observables introduced in Tables A-3 through A-5. These results are introduced in Table A-6. Usingthe empirically-grounded specification suggested in Oster (2017), we set the δ parameter to 1 and Rmax equalto 1.3× the R2 observed in the fully controlled specification. Notice that the test produces two solutions,both of which are below zero, consistent with our main specification.

20Results in these two tables are highly consistent (though not exactly the same) because the constantterm in Table A-10 absorbs nearly all of the level shift before the logarithm is evaluated.

22

from reanalysis data. Our climatic data are drawn from the National Centers for Envi-

ronmental Prediction (NCEP) and the Department of Energy, which prepared the baseline

climate reanalysis by using state-of-the-art assimilation techniques. These data are derived

from reanalysis (climate modeling) of underlying meteorological data. These techniques and

the data generation processes are fully described in Saha et al. (2010), to which we direct

interested readers. We then construct parameters capturing the number of days within each

growing season these data fall within a particular set of binned ranges. Using this tech-

nique enables us to flexibly account for non-linear relationships between weather conditions

and agricultural productivity. We supplement this data with information from Food and

Agriculture Organization’s Harmonized World Soil Database, which we extract using the

district-level cross section. We include nutrient availability, nutrient retention, rooting con-

ditions, oxygen availability, excess soil salts, toxicity, and packedness and workability (which

impacts the ability to manage fields). For each district, we calculate the percentage of land

mass where these soil features present no or slight limitations to productivity (Class 1 under

the FAO guidelines). Because various combinations of weather and soil conditions may pro-

duce high and low productivity zones in a complex system, we interact these measures with

our degree-day and precipitation-day measures. We merge these data with our panel data

on opium production and produce a standardized fitted value of opium productivity given

these exogenous parameters. We use the least squares estimation equation below.

log(productiond,y + 1) = α +7∑i=1

(ϑiPrecip−Dayd,y) +7∑i=1

(ζiPrecip−Day2d,y)

+10∑i=1

(ηiTemp−Dayd,y) +10∑i=1

(ρiTemp−Day2d,y) +

7∑i=1

(µiSoilQuald)

+ τij

7∑i=1

(Precipd,y)×7∑j=1

(SoilQuald) + υij

7∑i=1

(Precip2d,y)×

7∑j=1

(SoilQuald)

+ φij

10∑i=1

(Temp−Dayd,y)×7∑j=1

(SoilQuald) + ψij

10∑i=1

(Temp−Day2d,y)×

7∑j=1

(SoilQuald)

+ γXy + εd(2)

Where log(productiond,y + 1) is the production (log) for a given district, d, and grow-

ing season, y (year). Xy captures growing season fixed effects. Precip − Dayd,y and

Temp − Dayd,y capture the effect of our precipitation-day and degree-day (temperature-

day) parameters. See Figure A-1 for the binned ranges used in the analysis. We also include

23

the square of this counts. SoilQuald captures the soil quality features noted above. We then

fully interact these base terms. From this regression, we produce ̂log(productiond,y + 1),

which is our unstandardized fitted value. Denote this value as Λd,y. We standardize this

value using the following expression:

suitabilityd,y =Λd,y − Λ̄d,y

var(Λy)−1(3)

suitabilityd,y is demeaned and standardized with respect to the standard deviation of

the fitted values. This approach is most similar to Mej́ıa and Restrepo (2014), who use

land features and soil characteristics to predict coca production in Colombia. The primary

difference between our two methods is the use of high frequency climatic inputs as well as the

use of interactions to capture heterogeneous climatic effects via soil quality conditions. In

supplemental results, we use machine learning for vector reduction, in line with Rozenas and

Zhukov (2019). National price variation is not driven by any single district, which means

that all districts are effectively price-takers. Although not strictly necessary in our case

for identification, UNODC reports suggest the primary driver of current prices is aggregate

(national-level) production in the prior year. Naturally, increased aggregate production

from the prior year drives down national prices in the subsequent year. This gives us an

opportunity to instrument for the price component of revenue (once we invert the value),

which we implement below.21

5.2.2 Plausibility of Identifying Assumptions

We anticipate the exclusion restriction is plausibly satisfied for several reasons. First, we

use growing season agronomic conditions, which are observed months ahead of the beginning

of the fighting season. Given our non-parametric specification, which uses degree-day and

precipitation-day measures and soil suitability, it would be difficult to articulate a clear

pathway through which our measures of weather conditions directly impact combat timing.

Second, even if such a violation was econometrically plausible and induced non-trivial bias,

we expect this bias would be largely absorbed by accounting for variation in the levels

of combat activity during the fighting season, which is one of our benchmark parameters.

For a violation of the exclusion restriction to significantly bias our results, our growing

season agronomic inputs would have to have a persistent effect, that passes through our

non-parametric specification and subsequent dimensionality reduction, and is not absorbed

by our included covariates. We believe this is unlikely to be a substantial source of bias.

21The base term of aggregate production is absorbed in our fixed effects.

24

One plausible channel through which the independence assumption might be violated is

if, conditional on observing fluctuations in agronomic suitability, government forces strate-

gically reallocate aid projects. If these aid projects effectively reduce opium production (via

‘alternative livelihoods’ programming) and enhance local employment, our second stage ef-

fects are biased towards zero due to increasing reservation wages. It is also possible, however,

that rebels are able to capture some of the rents associated with aid projects. This could bias

our estimates upward, since the instrument potentially captures variation in opium revenue

correlated with both revenue channels. We address these concerns in the Online Appendix

using declassified data from the Commander’s Emergency Response Program (CERP). In

Table A-12, we replicate the benchmark model and include measures of aid intensity overall

and with respect to agricultural and irrigation projects only (dollars of aid delivered during

the growing season, ln). The main effects are slightly larger when incorporating overall aid

and slightly attenuated when limiting our focus to agricultural aid, neither of which are

statistically different from our benchmark result.

In Table A-13, we find strong evidence of a positive correlation between our suitability

index and annual revenue from the opium trade. Because we are accounting for potential

heteroskedasticity by district, we produce Kleibergen-Paap F statistic for our excluded in-

strument, which is well above 10. This suggests our instrument is relevant and strong. In

Table A-16, we investigate whether the monotonicity assumption is plausible with respect

to irrigation. This channel is relevant since our instrument captures exogenous variation

in suitability. How revenue responds (via production) to suitability may be a function of

technologies used to enhance productivity under otherwise poor agronomic conditions. For

example, it is possible that districts with varying levels of irrigation access (via canals and

other technology) will comply with the instrument at different rates. To assess monotonicity,

we gather data collected by FAO prior to the US invasion documenting irrigated sites. We

use this data to classify districts along the 75, 90, and 95 percentiles for the main estimating

sample and full panel. We find no clear evidence of weakened compliance with the instrument

via the irrigation mechanism.22

5.2.3 IV Results

We next turn to our main IV results. We report our second stage estimates in Table 4.

These results suggest the effect of revenue on temporal clustering of combat operations

22The corresponding second stage estimates are also statistically indistinguishable across these modelspecifications (relative the benchmark).

25

is substantially larger than our least squares estimates. One potential explanation for the

increasing magnitude of the effect relative to the baseline OLS specification is the presence of

cross-cutting dynamics with respect to counterinsurgent operations that we do not observe.

If counterinsurgents observe variation in opium production (or some endogenous subset),

they may strategically reallocate their forces or adjust their combat strategies. If these

changes in government activity also make it more difficult to acquire intelligence or mobilize

fighters, the per-unit change in rebel tactics due to opium revenue will be lower (i.e., biased

towards zero). While we observe some types of military operations, others that are perhaps

more relevant to rebel attack timing are unobserved (e.g., secret or top secret missions to

eliminate leaders). Our instrument may capture the subset of variation in opium production

that counterinsurgents find most difficult to anticipate, since it is unrelated to more readily

available information about rebel activity. Stated differently, our instrument perhaps helps

us identify opium production that is least predictable from a tactical military perspective.

Exploiting variation in revenue that is exogenous to government countermeasures therefore

increases the magnitude of the estimated effect of revenue on tactics.23

We next address three potential concerns about our IV approach. First, it is possible

that our estimation of opium suitability is overly saturated by a large number of agronomic

inputs. We do not anticipate that this represents an inferential concern. We allow for a

large number of input parameters because it enables our model of opium productivity to

be flexibly non-linear. This approach is common precisely because it limits the number of

functional form assumptions needed when predicting output at a granular level. This is also

ideal since we lack a well-developed agricultural model of poppy plants that is specific to

the context we study. That said, one alternative to our baseline approach is to use LASSO

estimation to reduce the number of input parameters in our model. By design, this limits

against oversaturation of the suitability model by eliminating a large number of potentially

irrelevant agronomic inputs. We reproduce our second stage results using LASSO-based

instrument in Table 5. Our F statistics suggest the IV remains strong. Compared with our

benchmark IV results, the main effect is slightly attenuated, though the two point estimates

are statistically indistinguishable.

A second potential concern is that our suitability model uses all available data on opium

production. Put differently, we have not withheld any elements of the raw data when con-

structing our index. Without holding some of our sample back, it is difficult to assess whether

23Naturally, we do not have data on unobserved missions, which could be used to further evaluate thispotential mechanism for the shift in our estimated coefficients.

26

some subset of the full panel is driving our estimated productivity. To address this concern,

we repeatedly estimate suitability (100 times), randomly holding back a subset (75%) of the

full panel. We then reproduce our second stage estimates. These results are visualized in

Figure 7. Notice that the second stage coefficient of our benchmark IV approach, noted as a

vertical line, is the median estimate of the full distribution of coefficients from the resampling

technique. Indeed, all second stage estimates based on sufficiently strong first stages (where

the F statistic is at least 10) are within .025 of the main coefficient. This suggests that our

main result is representative of the range of results that could be estimated given a large

number of arbitrary samples used to produce our suitability measure.

Yet a third possibility is that we could simply use the raw inputs for our suitability index

to instrument for opium revenue. This would effectively bypass the intermediate step where

we use raw productivity and agronomic inputs to estimate the district-season production

frontier (opium suitability). The central motivation for our main specification, which uses

a single estimate of opium suitability as an instrument for revenue, is to avoid the use of

many, potentially weak instruments. Alternatively, we could limit our first stage to the

baseline degree-day and precipitation-day agronomic inputs as instruments, and reestimate

our second stage results. We do this in Table 6. This approach allows us to address potential

concerns about misspecified standard errors in the first stage of the benchmark model, which

uses an estimated quantity as one component of the instrument,24 and enables us to explore

the plausibility of the estimated effects of agronomic conditions on opium production (via

revenue). In Table 6, notice that our point estimates, while slightly attenuated relative

our benchmark IV specification, are statistically indistinguishable from the baseline results.

The relevant F statistics are above 40, suggesting that our first stage is sufficiently strong

to estimate meaningful second stage effects. In the Online Appendix, we report the first

stage effects of agronomic inputs on opium revenue. These results (see Figure A-1 below)

are highly consistent with qualitative evidence from the UNODC, which suggests opium in

Afghanistan grows optimally in the presence of water access and warm conditions. Freezing

conditions during the growing season, associated with ground frost and snow cover, also

negatively impact productivity (see coefficient estimated for degree-days below 275 Kelvin

(equivalent to approximately 35 degrees Fahrenheit or 1 degree Celsius).25

By leveraging ‘as if’ random variation in high frequency, microlevel opium suitability,

the battery of instrumental variable approaches above give us more confidence that opium

24We thank Yuri Zhukov for suggesting this clarification.25See Kienberger et al. (2017) and the 2014 UNODC annual Opium Survey for more details regarding

suitable agronomic conditions for opium production in Afghanistan.

27

revenue influences temporal clustering in rebel attacks. Our IV estimates help us sidestep po-

tential concerns about endogenous variation in revenue driven by the production of violence

prior to the beginning of the fighting season.

6 Mechanisms

Having addressed numerous potential threats to identification, we now turn our attention

to a more direct test of our model’s empirical implications. Our results could be working

through at least two plausible mechanisms. First, revenue from the opium trade could give

field commanders more flexibility to recruit and arm fighters. This would enable them to

engage in combat operations where the timing of attacks is less random and, therefore,

easier for state rivals to anticipate and engage in strategic adjustment. As such, battlefield

losses are likely. These losses are more easily absorbed if a given rebel division has more,

better armed combatants. Second, increasing capacity could make it easier for insurgents to

deploy spies or buy information about troop movement patterns from civilians. Responding

strategically to intelligence reports about time windows within which troops and bases are

vulnerable could lead to temporal clustering. Importantly, these are not rival mechanisms.

They can operate simultaneously.

6.1 Intelligence Gathering by Rebels

Our data provides us with a unique opportunity to investigate the second mechanism more

precisely. In particular, we expect that conditions that make intelligence gathering easier

(i.e., reduced frictions) should enhance the negative effect of opium revenue on randomness

of combat. That is, in places where rebels have the ability to gather information about

troop and base vulnerabilities, temporal clustering should be even more responsive to rents

extracted from the opium trade.

We begin with the simplest test of this mechanism. We gather administrative data on

the distribution of ethnic groups across districts. We identify districts where 95% or more

of population settlements are classified as Pashto speaking. Pashtuns are Taliban coethnics

and form the primary base of civilian support for the insurgency. In principle, we expect

it will be easier for insurgents to acquire information about government activity in districts

dominated by their coethnics. We present these results in Table 7. Notice that the additive

effect of opium revenue in coethnic zones is much larger (roughly 80%) than non-coethnic

28

districts. This is evidence consistent with our story, but relying on coethnicity as a test of

our argument may conflate intelligence frictions with a range of other factors as well.

We overcome this concern by turning to more sophisticated tests of our argument. In

particular, our military records include previously unreleased information about rebel surveil-

lance of troop movement and base activity as well as data on security breaches, which occur

when insurgents are able to effectively infiltrate the outer perimeter of targets and observe

activity from within bases and outposts. These yield another potential test of our informa-

tion mechanism by tracking incidents where the Taliban are able to ‘turn’ security recruits

and use them to launch attacks from within army units. In each of these cases, we are

able to employ much more direct evidence of the ability of the insurgency to gather precise

information about target defenses. We test our mechanism using these data in Columns

2 through 5 in Table 8. In Column 2, we interact our measure of the spy network opera-

tions with revenue.26 In the Online Appendix, we repeat this specification with measures of

infiltration and insider attacks (see Tables A-24 and A-25). We find strong evidence that

our main effect is enhanced in districts where the insurgents have a demonstrated capability

to conduct surveillance, infiltrate security installations, and launch insider attacks. These

findings yield evidence consistent with the mechanism implied by our theoretical argument

and suggest that intelligence gathering may be a primary pathway through which shocks to

rebel capacity influence the timing of violent attacks.

6.2 Labor Scarcity

We suggest that revenue shocks may impact combat tactic through the ability to mobilize

fighters. Unfortunately, we lack sufficiently granular census data on the size of Taliban sub-

units to fully assess the direct effects of budget constraints on recruitment and deployment.

However, we can investigate this mechanism through an alternative approach: battlefield

losses experienced during combat operations. The intuition of this test is in line with the

mechanism we theorize. As insurgents accumulate resources, they can mobilize more fighters,

enabling them to adopt tactics that would otherwise be too costly from a human capital per-

spective. If attacks are predictably launched, government forces can deploy relatively more

effective countermeasures, potentially neutralizing some subset of fighters through casual-

ties. For relatively weak insurgents, these costs may be too great, leading them to conduct

attacks that are randomized and more difficult to thwart.

26To avoid potential concerns about the endogeneity of intelligence gathering, we identify the cross sectionof districts with these characteristics using only the first year of our sample, 2006.

29

Although we cannot directly examine whether revenue shocks lead to expansion of rebel

forces, we can study whether labor constraints (via lost fighters) lead to a change in tac-

tics. The intensity of potential battlefield losses is increasing in combat activity, which our

model accounts for in levels via fighting season activity for indirect fire attacks. However,

because battlefield losses are most common in direct combat (when rebels are engaged in

close combat with military units), we introduce an additional parameter to our benchmark

model capturing the overall intensity of combat activity across the three primary categories

of combat. Adding this parameter allows us to partial out any variation in labor scarcity

(casualties) due to the intensity of combat operations, yielding plausibly abnormal variation

in battlefield losses. We present these results in Table 9. Notice that battlefield losses (posi-

tive coefficient) lead to an increase in randomization. The estimated effect on labor scarcity

suggests a one standard deviation increase in losses leads to a .12 standard deviation increase

in randomization.

A natural concern is that battlefield losses, even after conditioning on combat activity

(in levels), are not sufficiently ‘as if’ random to draw causal inferences. We attempt to

address this concern in the online appendix, where we add our measures of counterinsurgent

operations (from Tables A-3 and A-4), which are the most plausible omitted variables in this

regression. We introduce these results in Table A-26. Once we account for these omitted

factors, our results get larger in magnitude, giving us more confidence in the main results in

Table 9.

6.3 Government Surveillance

We conclude the discussion of the mechanisms by returning to the role of surveillance. We

argue that revenue generation by insurgents eases constraints on intelligence gathering, mak-

ing it easier for rebels to identify time periods during which government forces are vulnerable.

If, on the other hand, government forces are capable of and conduct operations to monitor

rebel activity, they may be more likely to identify patterns in rebel attacks. Information

about when insurgents are likely to launch attacks as well as other features of militia opera-

tions enables government forces to directly thwart rebel operations and disrupt their combat

planning. Our data gives us another unique opportunity to explore this channel: we observe

where and how frequently government forces are actively monitoring insurgent tactics and

procedures during the fighting season. We replicate the model above, accounting for the

confounding correlation between combat activity and the allocation of surveillance assets.

These results are presented in Table 10. Notice that, as our theoretical model anticipates, in-

30

creased government monitoring is associated with more attack randomization (less temporal

clustering).

7 Battlefield Consequences of Temporal Clustering

In this section, we consider several battlefield outcomes associated with temporal clustering

of rocket fire attacks. Mortar and rocket fire rarely cause physical combat casualties but

can cause mental or psychological harm.27 Crocq and Crocq (2000) describe that concussive

forces from shelling, rocket, and mortar fire have had well-documented effects on soldier

psychological health during modern military engagements. Symptoms during World Wars I

and II included muteness, dizziness, hyper-sensitivity to sound, aggression, and depressive

episodes (Andreasen, 2011).

Psychological harm can reduce cognitive dexterity, accelerate fatigue during battle op-

erations, and impair coordination between soldiers during patrols and active engagements.

Afari et al. (2015) report that the most common type of combat exposure for male and female

combatants during Operation Enduring Freedom in Afghanistan was receiving rocket or mor-

tar fire and present evidence that combat exposure increased symptoms of post-traumatic

stress disorder, depression, verbal aggression, and heightened interpersonal aggression after

soldiers returned from deployment. If insurgents calibrate their attack timing to exploit sol-

dier and infrastructure vulnerabilities, temporal clustering may have profound consequences

for soldier mental health.28 Although these effects are difficult to examine directly during

active deployments, we can assess whether temporal clustering of mortar attacks decreases

soldier efficiency once military forces leave the base to conduct patrol-based operations.29

One critical category of these operations is ‘find and clear’ missions, where soldiers identify

and neutralize roadside bombs. Reduced soldier efficiency would correspond to fewer bombs

cleared from the battlefield. If efficiency of these patrol-based operations is reduced enough,

it may trigger increased casualties due to bombs that soldiers could have but did not discover

and neutralize. We can test both of these conjectures with our military records.

In both of these cases, our outcome of interest is battlefield outcomes (bombs found and

cleared and bomb-induced casualties) and our quantity of interest is now the temporal clus-

tering parameter that was previously our dependent variable. We replicate the benchmark

27Coalition forces were killed in action during 69 of 28,617 indirect fire attacks compared with 1001 fatalroadside bomb detonations (out of 37,936).

28We thank Michael Gilligan for sharpening this point.29We thank Jacob Shapiro and Alex Weisiger for this suggestion.

31

specification in Table 1. The first set of results on soldier efficiency are reported in Table 11.

Recall, larger values of the randomization parameter correspond to a more random allocation

of attacks across time. If our conjecture is correct, we would expect a positive correlation

between the randomization parameter and successful missions. Indeed, this is what we find

(Column 1). As attacks become more random, there are more successful ‘find and clear’

missions. Stated differently, as indirect fire attacks become more temporally clustered, the

number of successful clearance missions goes down. The benchmark specification partials

out fighting season fixed effects as well as variation in district-specific IED deployment in

levels during the fighting season. Our results are highly consistent if we also account for

indirect fire activity during the fighting, growing, and planting seasons (Columns 2-4). To

further assess this mechanism, we can test whether bomb-induced casualties increase as at-

tacks become more temporally clustered. Since our outcome now effectively tracks a type of

mission ‘failure’, we expect the correlation with our randomness measure will be negative.

If the correlation is negative, it suggests increased temporal clustering (lower values of the

explanatory variable) correspond to more bomb-induced casualties. This is what we find in

Table 12. Taken together, these results provide evidence that clustering of attack timing

significantly reduces government soldier efficiency and increases risks to deployed troops.

8 Extensions

In this section, we study several extensions which clarify the industrial organization of re-

bellion and yield potentially actionable insights about insurgent operations.

8.1 Reservation Wages

To study the relative impact of reservation wages, we take advantage of an important feature

of the context of our study: differential taxation. At baseline, we anticipate Taliban fighters

collect a flat (typically 10%) tax on opium proceeds. Qualitative documents suggest the

bureaucracy established to manage these transactions is sophisticated and repeated taxation

(‘double taxation’) and excessive taxation are prohibited. However, the Taliban cannot fully

control how much local politicians—agents of the formal government—extract as informal

taxes (Giustozzi, 2009; Mansfield, 2016). In the absence of these secondary taxes, gains from

the opium trade translate into simultaneous growth in rebel capacity and growth in the local

economy. As such, resources available to compensate fighters and spies and local reservation

wages may be increasing in revenue. This will lead to a cross-cutting effect that biases

32

our estimate towards zero, since increasing reservation wages offset some of the impact of

revenue growth on mobilization, recruitment, and, by extension, combat tactics. To better

disentangle these effects, we need to identify locations where informal taxes absorb some of

the growth in the local economy which influences reservation wages.

We do this by taking advantage of proprietary military surveys provided to the authors

by the North Atlantic Treaty Organization (NATO).30 These surveys enable us to quantify

the level of corruption present in local administrative agencies across Afghanistan.31

We anticipate that revenue growth will have larger effects in places with more severe cor-

ruption, where reservation wages grow at a slower rate due to informal taxation. We present

these results in Table 13. Consistent with our expectations, in districts with corruptible

politicians where reservation wages remain relatively lower, we see larger marginal effects

over the baseline condition (with relatively less informal taxation).

8.2 Savings Technologies

We next consider whether local rebel units utilize savings technologies to engage in consump-

tion smoothing. Revenue from the opium trade can be volatile, with droughts, crop diseases,

and other unpredictable factors negatively impacting productivity from season to season.

In response, units within the Taliban may engage in consumption smoothing, holding back

some of their fighting capacity for the next season in expectation of uncertainty regarding

future revenue. To assess this dynamic, we use our full panel data on revenue to calcu-

late income volatility for each district. We then split districts into high and low volatility

30We utilize the Afghanistan Nationwide Quarterly Research (ANQAR) survey. ACSOR, an Afghan sub-sidiary of the international firm D3, was contracted to design and field the survey. ACSOR hired and trainedlocal enumerators in household and respondent selection, how to correctly record answers to questions, cul-turally sensitive interview methods, and secure storage of contact information. The administrative district(the cross section unit in this study) is the primary sampling unit. These sampling units are selected viaprobability proportional to size systematic sampling approach. After districts have been sampled, secondarysampling units composed of villages and settlements are randomly selected. A random walk method is usedto identify target households and a Kish grid is used to randomize the respondent within each selectedhousehold. After the sampling set has been identified and before fielding a survey wave, ACSOR engageswith local elders to secure permission for enumerators to enter sample villages. See Condra and Wright(Forthcoming) for more details and diagnostics.

31We split districts into low versus high corruption categories based on the percentage of respondentsacross all available waves which describe corruption in government as a very serious problem. If more thanone third report corruption as very serious, we classify the district as corrupt (and local administrators ascorruptible). This equates to the tenth percentile of the overall distribution. Results are consistent if we usea lower threshold.

33

clusters.32 If rebels engage in consumption smoothing, we would expect combat tactics to

be less responsive per unit of income growth in high volatility districts. We estimate these

heterogeneous effects in Table 14. Notice that the high income volatility does not lead to

a marginally smaller effect on combat. This suggests that rebels do not actively engage in

smoothing across seasons; rebels likely exhaust available resources during the fighting season

immediately following tax collection.

9 Conclusion

Rebel tactics are an overlooked feature of internal warfare. Understanding how these con-

flicts are fought and the strategic responses of armed actors to revenue shocks is on equal

footing with thoroughly examined questions about the causes of civil war and the factors

that influence when hostilities end.

We argue that shocks to rebel capacity influence the timing of attacks. We develop a

simple model of combat during an irregular insurgency. Rebels optimize when they conduct

attacks after observing imperfect signals of government defensive maneuvers. As insur-

gents accumulate resources through taxation, their budget constraint is relaxed and they

can recruit more fighters, acquire more armaments, and gather more intelligence about the

vulnerability of troops and bases. The labor supply of fighters, coupled with surplus capi-

tal, allows rebels to conduct more attacks. Infiltrating military installations and conducting

surveillance of troop movement enhances the quality of information rebels have about spe-

cific times when attacks will yield the highest probability of success. Thus, revenue shocks

will lead to clustering in the temporal distribution of violence. Our model also suggests that

these tactical shifts will be greatest when armed actors have the institutional capacity to

pin-point when such attacks are least likely to be neutralized by government defenses.

We test the empirical implications of our theoretical model using data collected during

Operational Enduring Freedom in Afghanistan. The temporal precision of our military

records enable us to develop a sophisticated methodology for differentiating the within-day

timing of rebel operations from randomized combat. This method produces a likelihood

parameter that quantifies the degree of temporal clustering present in the allocation of

insurgent attacks at the district level, broken down by fighting season. We couple this novel

approach with high resolution estimates of opium production and market prices. We leverage

32We classify districts into these categories using the median level of volatility observed among opiumproducing districts in the full panel.

34

the industrial organization of the Taliban, including their highly institutionalized taxation

system, to estimate the impact of local revenue from the drug trade on combat tactics in

the subsequent fighting season.

Our evidence suggests that the randomness of attacks significantly decreases as rebels

accumulate more resources from the opium trade. As rebels accumulate fighting capacity,

their attacks become temporally clustered around particular time windows in the day. This

core result survives a number of robustness checks, including accounting for trends in rebel

violence during the fighting, harvest, and planting seasons, which may influence the intensity

of opium cultivation from year to year. The richness of our microdata also enables us to rule

out additional concerns about the positive covariance between rebel capacity and strategic

reallocation of government forces.

Our data also yields a unique opportunity to assess the underlying mechanism suggested

by our model: intelligence gathering. Temporal clustering occurs because rebels use their

resources to improve the quality and precision of their information about target vulnerability.

This type of mechanism is largely unobserved and difficult to disentangle from alternative

explanations. Our military records, however, include detailed information about where rebels

were observed conducting surveillance operations as well as instances where insurgents were

able to infiltrate government installations and conduct insider attacks. The capacity to

gather intelligence substantially enhances the baseline effect of revenue shocks on combat

operations. These effects are reversed when rebels experience battlefield losses or government

surveillance.

We conclude our empirical results by highlighting the battlefield consequences of temporal

clustering in attack patterns. We find robust evidence that increased combat clustering in

time reduces soldier efficiency by decreasing the number of successful ‘find and clear’ missions

and increasing the number of bomb-induced battlefield casualty events. Taken together,

these results suggest that insurgents engage in institutionalized rent extraction and use

these resource shocks to gather intelligence about government vulnerabilities, calibrate their

combat tactics, and enhance their military effectiveness.

35

References

Abadie, Alberto. 2002. “Bootstrap Tests for Distributional Treatment Effects in InstrumentalVariable Models.” Journal of the American Statistical Association 97(457):284–292.

Abadie, Alberto and Javier Gardeazabal. 2003. “The Economic Costs of Conflict: A CaseStudy of the Basque Country.” American Economic Review 93(1):113–132.

Afari, Niloofar, James Pittman, Elizabeth Floto, Laura Owen, Melissa Buttner, Nazia Hos-sain, Dewleen G. Baker, Laurie Lindamer and James B. Lohr. 2015. “Differential Im-pact of Combat on Postdeployment Symptoms in Female and Male Veterans of Iraq andAfghanistan.” Military Medicine 180(3):296–303.

Andreasen, Nancy C. 2011. “What is post-traumatic stress disorder?” Dialogues in ClinicalNeuroscience 13(3):240–243.

Bazzi, Samuel and Christopher Blattman. 2014. “Economic shocks and conflict: evidencefrom commodity prices.” American Economic Journal: Macroeconomics 6(4):1–38.

Beath, Andrew, Fotini Christia and Ruben Enikolopov. 2013. Winning Hearts and Mindsthrough Development: Evidence from a Field Experiment in Afghanistan. In APSA 2013Annual Meeting Paper.

Berman, Eli and Aila M. Matanock. 2015. “The Empiricists’ Insurgency.” Annual Review ofPolitical Science 18:443–64.

Berman, Eli, Michael Callen, Joseph H. Felter and Jacob N. Shapiro. 2011. “Do WorkingMen Rebel? Insurgency and Unemployment in Afghanistan, Iraq, and the Philippines.”Journal of Conflict Resolution 55:496–528.

Berman, Nicolas, Mathieu Couttenier, Dominic Rohner and Mathias Thoenig. 2017. “ThisMine Is Mine! How Minerals Fuel Conflicts in Africa.” American Economic Review107(6):1564–1610.

Berrebi, Claude and Esteban F Klor. 2008. “Are voters sensitive to terrorism? Directevidence from the Israeli electorate.” American Political Science Review 102(3):279–301.

Besley, Timothy and Hannes Mueller. 2012. “Estimating the Peace Dividend: The Impact ofViolence on House Prices in Northern Ireland.” American Economic Review 102(2):810–33.

Besley, Timothy and Torsten Persson. 2010. “State capacity, conflict and development.”Econometrica 78:1–34.

Besley, Timothy and Torsten Persson. 2011. “The Logic of Political Violence.” The QuarterlyJournal of Economics 126(3):1411–1445.

36

Blackett, D. W. 1958. “Pure Strategy Solutions of Blotto Games.” Naval Research LogisticsQuarterly 5(2):107–109.

Borel, Emil. 1921. “La theorie du jeu les equations integrales a noyau symetrique. ComptesRendus del Academie, 173, 1304-1308; English translation by Savage, L. (1953). The theoryof play and integral equations with skew symmetric kernels.” Econometrica 21:97–100.

Bueno de Mesquita, Ethan. 2013. “Rebel tactics.” Journal of Political Economy 121(2):323–357.

Callen, Michael, Mohammad Isaqzadeh, James D. Long and Charles Sprenger. 2014. “Vi-olence and Risk Preference: Experimental Evidence from Afghanistan.” American Eco-nomic Review 104(1):123–148.

Carter, David. 2015. “When terrorism is evidence of state success: securing the state againstterritorial groups.” Oxford Economic Papers 2014:1–17.

Collier, Paul and Anke Hoeffler. 2004. “Greed and grievance in civil war.” Oxford EconomicPapers 56(563-595).

Condra, Luke and Austin Wright. Forthcoming. “Civilians, Control, and Collaborationduring Civil Conflict.” International Studies Quarterly .

Condra, Luke N. and Jacob N. Shapiro. 2012. “Who Takes the Blame? The Strategic Effectsof Collateral Damage.” American Journal of Political Science 56(1):167–187.

Condra, Luke N., James D. Long, Andrew C. Shaver and Austin L. Wright. 2018. “TheLogic of Insurgent Electoral Violence.” American Economic Review 108(11):3199–3231.

Crocq, M A and L Crocq. 2000. “From shell shock and war neurosis to posttraumatic stressdisorder: a history of psychotraumatology.” Dialogues in lCinical Neuroscience 2(1):47–55.

Dal Bo, Ernesto and Pedro Dal Bo. 2011. “Workers, Warriors, and Criminals: Social Conflictin General Equilibrium.” Journal of the European Economic Association 9(4).

Dube, Oeindrilla and Juan Vargas. 2013. “Commodity price shocks and civil conflict: evi-dence from Colombia.” Review of Economic Studies 80:1384–1421.

Esteban, Joan and Debraj Ray. 2011. “Linking Conflict to Inequality and Polarization.”American Economic Review 101(4):1345–74.

Esteban, Joan, Laura Mayoral and Debraj Ray. 2012. “Ethnicity and Conflict: An EmpiricalStudy.” American Economic Review 102(4):1310–42.

Esteban, Joan, Massimo Morelli and Dominic Rohner. 2015. “Strategic Mass Killings.”Journal of Political Economy 123(5):1087–1132.

37

Fearon, James and David Laitin. 2003. “Ethnicity, insurgency and civil war.” AmericanPolitical Science Review 97(1):75–90.

Galula, David. 1964. Counterinsurgency Warfare: Theory and Practice. New York: Praeger.

Gehring, Kai, Sarah Langlotz and Stefan Kienberger. 2019. “Stimulant or Depressant?Resource-Related Income Shocks and Conflict.”.

Gennaioli, Nicola and Hans-Joachim Voth. 2015. “State Capacity and Military Conflict.”The Review of Economic Studies 82(4):1409–1448.

Getmansky, Anna and Thomas Zeitzoff. 2014. “Terrorism and voting: The effect of rocketthreat on voting in Israeli elections.” American Political Science Review 108(3):588–604.

Giustozzi, Antonio. 2009. Empires of Mud: wars and warlords in Afghanistan. New York:Columbia University Press.

Golman, Russell and Scott E. Page. 2009. “General Blotto: games of allocative strategicmismatch.” Public Choice 138(3):279–299.

Gould, Eric D. and Esteban F. Klor. 2010. “Does Terrorism Work?*.” The Quarterly Journalof Economics 125(4):1459–1510.

Goyal, Sanjeev and Adrien Vigier. 2014. “Attack, Defence, and Contagion in Networks.”Review of Economic Studies 81(4):1518–1542.

Hidalgo, Daniel, Suresh Naidu, Simeon Nichter and Neal Richardson. 2010. “Economicdeterminants of land invasions.” Review of Economics and Statistics 92(3):505–523.

Hillion, Erwan and Oliver Johnson. 2017. “A proof of the SheppOlkin entropy concavityconjecture.” Bernoulli 23(4B):3638–3649.

Jia, Ruixue. 2014. “Weather shocks, sweet potatoes and peasant revolts in historical China.”The Economic Journal pp. 92–118.

Kalyvas, Stathis N. 2006. The Logic of Violence in Civil War. New York: CambridgeUniversity Press.

Kienberger, Stefan, Raphael Spiekermann, Dirk Tiede, Irmgard Zeiler and Coen Bussink.2017. “Spatial risk assessment of opium poppy cultivation in Afghanistan: integrating envi-ronmental and socio-economic drivers.” International Journal of Digital Earth 10(7):719–736.

Konig, Michael D., Dominic Rohner, Mathias Thoenig and Fabrizio Zilibotti. 2017. “Net-works in Conflict: Theory and Evidence From the Great War of Africa.” Econometrica85:1093–1132.

38

Konrad, Kai A. and Dan Kovenock. 2009. “Multi-battle contests.” Games and EconomicBehavior 66(1):256–274.

Kovenock, Dan and Brian Roberson. 2012. “Conflicts with Multiple Battlefields,” in MichelleR. Garfinkel and Stergios Skaperdas (eds.). Oxford Handbook of the Economics of Peaceand Conflict, Oxford University Press, New York. pp. 503-531.”.

Kress, Moshe. 2012. “Modeling Armed Conflicts.” Science 336(6083):865–869.

Le Billon, Philippe. 2001. “The Political Ecology of War: Natural Resources and ArmedConflict.” Political Geography 20:561–584.

Limodio, Nicola. 2019. “Terrorism Financing, Recruitment and Attacks: Evidence from aNatural Experiment.” Chicago Booth Research Paper No. 32 .

Lind, Jo Thori, Karl Ove Moene and Fredrik Willumsen. 2014. “Opium for the masses?Conflict-induced narcotics production in Afghanistan.” Review of Economics and Statistics96(5):949–966.

Mansfield, David. 2016. A State Built on Sand: How Opium Undermined Afghanistan.Oxford: Oxford University Press.

Mej́ıa, Daniel and Pascual Restrepo. 2014. “Bushes and bullets: illegal cocaine markets andviolence in Colombia.” Working paper.

Miguel, Edward, Shanker Satyanath and Ernest Sergenti. 2004. “Economic shocks and civilconflict: an instrumental variables approach.” Journal of Political Economy 112(4):725–753.

Oster, Emily. 2017. “Unobservable Selection and Coefficient Stability: Theory and Evi-dence.” Journal of Business & Economic Statistics 0(0):1–18.

Padro i Miquel, Gerard and Pierre Yared. 2012. “The Political Economy of Indirect Control.”The Quarterly Journal of Economics 127(2):947–1015.

Perry, J. N. and R. Mead. 1979. “On the Power of the Index of Dispersion Test to DetectSpatial Pattern.” Biometrics 35(3):613–622.

Peters, Gretchen S. 2009. The Taliban and the Opium Trade. New York: Columbia UniversityPress pp. 7–22.

Powell, Robert. 2007a. “Allocating Defensive Resources with Private Information aboutVulnerability.” American Political Science Review 101(4):799–809.

Powell, Robert. 2007b. “Defending against Terrorist Attacks with Limited Resources.” Amer-ican Political Science Review 101(3):527–541.

39

Powell, Robert. 2013. “Monopolizing Violence and Consolidating Power.” Quarterly Journalof Economics pp. 807–859.

Roberson, Brian. 2006. “The Colonel Blotto game.” Economic Theory 29(1):1–24.

Roberson, Brian and Dmitriy Kvasov. 2012. “The non-constant-sum Colonel Blotto game.”Economic Theory 51(2):397–433.

Ross, Michael. 2004. “What do we know about natural resources and civil war?” Journal ofPeace Research 41:337–356.

Rozenas, Arturas and Yuri Zhukov. 2019. “Mass Repression and Political Loyalty: Evidencefrom Stalins Terror by Hunger.” American Political Science Review 113(2):569–583.

Saha, Suranjana, Shrinivas Moorthi, Hua-Lu Pan, Xingren Wu, Jiande Wang and et al. 2010.“The NCEP Climate Forecast System Reanalysis.” Bulletin of the American Meteorolog-ical Society 91(8):1015–1057.

Sexton, Renard. 2016. “Aid as a Tool against Insurgency: Evidence from Contested andControlled Territory in Afghanistan.” American Political Science Review 110(4):731–749.

Shaver, Andrew and Austin Wright. 2017. “Data on Combatant Activity During AfghanistanWar Advance Scientific Investigation of Insurgency.”.

Shayo, Moses and Asaf Zussman. 2017. “Conflict and the Persistence of Ethnic Bias.”American Economic Journal: Applied Economics 9(4):137–65.

Thompson, Robert. 1966. Defeating Communist Insurgency: The Lessons of Malaya andVietnam. New York: Praeger.

Trebbi, Francesco, Eric Weese, Austin Wright and Andrew Shaver. 2017. “Insurgent Learn-ing.” NBER Working Paper 23475 .

Vanden Eynde, Oliver. 2018. “Targets of Violence: Evidence from India’s Naxalite Conflict.”The Economic Journal 128(609):887–916.

Weidmann, Nils B. 2016. “A closer look at reporting bias in conflict event data.” AmericanJournal of Political Science 60(1):206–218.

Weinstein, Jeremy M. 2007. Inside Rebellion: The Politics of Insurgent Violence. Cambridge:Cambridge University Press.

Wood, Reed M. 2014. “Opportunities to Kill or Incentives for Restraint? Rebel Capabilities,the Origins of Support, and Civilian Victimization in Civil War.” Conflict Managementand Peace Science 31(5):461–480.

Wright, Austin L. 2016. “Economic Shocks and Rebel Tactics: Evidence from Colombia.”HiCN paper #232 .

40

Figure 1: Military records indicate the location of rebel surveillance operations conductedin Afghanistan (2006).

Notes: Data on insurgent spy operations drawn from SIGACTS military records. Cross hatch patternindicates insurgents conducted at least one detected surveillance operations during 2006, the first year of oursample. District boundaries are drawn from the ESOC Afghanistan map (398 districts).

41

Figure 2: UNODC Methodology for Estimating Annual District Drug Production.

(a) Sampling Satellite Imagery (b) Impute Production from Imagery/Field Obs.

Notes: Methodological figures and details drawn from the 2016 UNODC-Afghanistan Drug Report. Panel(a) demonstrates the sampling design used when acquiring high resolution satellite imagery (location: Kan-dahar). Panel (b) illustrates the subsequent production estimation, which combines low and high resolutionimagery (location: Nangahar).

Figure 3: Time series data on opium prices collected at national (a) and regional (b) levels.

(a) National price time series (b) Regional prices time series

Notes: Figures on national and regional price time series drawn from the 2016 UNODC-Afghanistan DrugReport. Underlying data compiled from farmer and market spot price surveys conducted throughout theyear. In Panel (a), the simple average is calculated (Nangahar, Kandahar). In Panel (b), we assign districtsto regions according the UNODC documentation. Prices were precisely extracted using WebPlotDigitzer.

42

Figure 4: Distribution of p-values from randomization test of combat in Afghanistan

0

.1

.2

.3

Den

sity

of p

-val

ues

-25 -20 -15 -10 -5 0Logarithm of p-values from KS test -- Indirect Fire Attacks

Figure 5: Bivariate relationship between opium revenue and p-value of randomization testof combat (indirect fire attacks) in Afghanistan

0

20

40

60

80

100

Opi

um re

venu

e

-25 -20 -15 -10 -5 0Logarithm of p-values from KS test -- Indirect Fire Attacks

Observed opium revenue/p-value Fit line with 95% CI

43

Figure 6: Randomization Inference to Evaluate Robustness of Benchmark Effect Adjustingfor Spatial Correlation

← Benchmark Effect

0

.02

.04

.06

.08

.1

Frac

tion

-.06 -.05 -.04 -.03 -.02 -.01 0 .01 .02 .03 .04 .05 .06Distribution of Estimated (Randomized) Effects

(a) Full Panel Reshuffling, Province Strata

← Benchmark Effect

0

.02

.04

.06

.08

.1

Frac

tion

-.06 -.05 -.04 -.03 -.02 -.01 0 .01 .02 .03 .04 .05 .06Distribution of Estimated (Randomized) Effects

(b) Full Panel Reshuffling, District Strata

Notes: We randomly reshuffle the opium revenue vector in our data using two approaches (× 1000). Weutilize observed opium revenue for the full panel of district-years and vary the spatial strata used for spatiallyconstrained randomization ((a) province, (b) district). The model specification is equivalent to Table 1,Column 4, with strata fixed effects.

Figure 7: Distribution of second stage IV estimates using random resampling technique toproduce alternate suitability instruments. Main effect noted with vertical line.

0

10

20

30

40

50

Dens

ity o

f Dist

ribut

ion

-.5 -.4 -.3 -.2 -.1 0Estimted Impact of Opium Revenue on Randomization of Attack Timing

All Instruments Strong Instruments

44

Table 1: Impact of rebel capacity on within-day randomization of indirect fire attacks

(1) (2) (3) (4)Opium Revenue -0.0581∗∗∗ -0.0588∗∗∗ -0.0549∗∗∗ -0.0549∗∗∗

(0.0137) (0.0135) (0.0125) (0.0125)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.154 0.171 0.187 0.187

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fightingseason fixed effects. Column 2-4 add controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Heteroskedasticityrobust standard errors clustered by district are reported in parentheses. Stars indi-cate *** p < 0.01, ** p < 0.05, * p < 0.1.

Table 2: Impact of rebel capacity on within-day randomization of indirect fire attacks,robustness checks

(1) (2) (3) (4) (5) (6)Opium Revenue -0.0549∗∗∗ -0.0450∗∗ -0.0531∗∗∗ -0.0543∗∗∗ -0.0381∗∗

(0.0125) (0.0220) (0.0116) (0.0126) (0.0166)Opium Revenue (Regional) -0.0555∗∗∗

(0.0128)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes Yes Yes YesAdditional ParametersProvince × Fighting Season FE No Yes No No No NoWeighted Least Squares No No Yes No No NoRegional Yield Adjust. No No No Yes No NoEarly Harvest Only No No No No Yes NoDistrict Fixed Effect No No No No No YesModel StatisticsNo. of Observations 600 600 600 600 588 563No. of Clusters 154 154 154 154 150 117R2 0.187 0.379 0.188 0.184 0.184 0.503

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest is opiumrevenue for a given district-year. All regressions include fighting season fixed effects as well as controls forthe intensive margin of fighting during the fighting, harvest, and planting seasons respectively. Additionalparameters are noted in the table footer. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

45

Table 3: Impact of rebel capacity on binary classifications of within-day randomization ofindirect fire attacks

(1) (2) (3) (4) (5)p ≤ .05(= 1)

p ≤ .01(= 1)

p ≤ .002(= 1) (Median)

p ≤ .001(= 1)

p ≤ .0005(= 1)

Opium Revenue 0.000567∗∗ 0.00256∗∗∗ 0.00492∗∗∗ 0.00531∗∗∗ 0.00485∗∗∗

(0.000269) (0.000519) (0.000765) (0.000862) (0.000874)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes Yes YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.0260 0.0927 0.0983 0.103 0.123

Notes: Outcome of interest is a column varying binary classification of districts using the p-value of therandomness test. Thresholds are noted in each column heading, with the center column representingthe median of the distribution. The quantity of interest is opium revenue for a given district-year. Allregressions include fighting season fixed effects as well as controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons. A one standard deviation increase in revenue fromthe opium trade increases the probability of being classified as a temporally clustered unit by 12.5% forthe median threshold. Heteroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

46

Table 4: Impact of rebel capacity on within-day randomization of indirect fire attacks,instrumental variables approach (second stage)

(1) (2) (3) (4)Opium Revenue -0.0793∗∗∗ -0.0787∗∗∗ -0.0741∗∗∗ -0.0741∗∗∗

(0.0271) (0.0268) (0.0247) (0.0247)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.136 0.155 0.173 0.173IV SpecificationIV Type Benchmark Benchmark Benchmark BenchmarkKleibergen-Paap F Statistic 190.9 188.4 188.9 187.4

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity ofinterest is opium revenue for a given district-year instrumented using an opium suitabilityindex interacted with the prior year’s national-level production (inverted). All regressionsinclude fighting season fixed effects as well as controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Additional parameters arenoted in the table footer. Heteroskedasticity robust standard errors clustered by districtare reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

47

Table 5: Impact of rebel capacity on within-day randomization of indirect fire attacks,instrumental variables approach (second stage) using LASSO selection in suitability indexestimation

(1) (2) (3) (4)Opium Revenue -0.0759∗∗∗ -0.0757∗∗∗ -0.0701∗∗∗ -0.0701∗∗∗

(0.0270) (0.0266) (0.0248) (0.0248)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.142 0.160 0.178 0.178IV SpecificationIV Type Lasso Lasso Lasso LassoKleibergen-Paap F Statistic 114.7 113.2 117.9 118.2

Notes: Outcome of interest is the (log) p-value of the randomness test. The quan-tity of interest is opium revenue for a given district-year instrumented using anopium suitability index interacted with the prior year’s national-level production(inverted). All regressions include fighting season fixed effects as well as controls forthe intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedastic-ity robust standard errors clustered by district are reported in parentheses. Starsindicate *** p < 0.01, ** p < 0.05, * p < 0.1.

48

Table 6: Impact of rebel capacity on within-day randomization of indirect fire attacks, instru-mental variables approach (second stage) using agronomic inputs as instrumental variables

(1) (2) (3) (4)Opium Revenue -0.0681∗∗∗ -0.0679∗∗∗ -0.0617∗∗∗ -0.0617∗∗∗

(0.0203) (0.0197) (0.0188) (0.0188)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.150 0.168 0.185 0.185IV SpecificationIV Type Agronomic Agronomic Agronomic AgronomicKleibergen-Paap F Statistic 44.56 42.48 44.48 44.43

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year instrumented using degree-day(temperature-day) and precipitation-day instruments. All regressions include fightingseason fixed effects as well as controls for the intensive margin of fighting during thefighting, harvest, and planting seasons respectively. Additional parameters are notedin the table footer. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

49

Table 7: Heterogeneous effects of rebel capacity on within-day randomization of indirect fireattacks with respect to potential intelligence gathering via coethnics

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0150∗∗ -0.0178∗∗ -0.0146∗ -0.0146∗

(0.0137) (0.00717) (0.00757) (0.00766) (0.00766)Coethnicity 0.246 0.288 0.378 0.378

(0.333) (0.329) (0.351) (0.352)Coethnicity × Revenue -0.0582∗∗∗ -0.0554∗∗∗ -0.0552∗∗∗ -0.0552∗∗∗

(0.0175) (0.0170) (0.0168) (0.0168)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.193 0.204 0.218 0.218

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

50

Table 8: Heterogeneous effects of rebel capacity on within-day randomization of indirect fireattacks with respect to potential intelligence gathering by spies

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0207∗∗∗ -0.0224∗∗∗ -0.0194∗∗∗ -0.0194∗∗∗

(0.0137) (0.00669) (0.00661) (0.00663) (0.00664)Surveillance 0.605∗ 0.758∗∗ 0.952∗∗ 0.953∗∗

(0.320) (0.337) (0.405) (0.400)Surveillance × Revenue -0.0671∗∗∗ -0.0669∗∗∗ -0.0678∗∗∗ -0.0678∗∗∗

(0.0193) (0.0191) (0.0190) (0.0191)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.206 0.219 0.233 0.233

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

51

Table 9: Effects of rebel capacity and battlefield losses on within-day randomization ofindirect fire attacks

(1) (2) (3) (4) (5)Opium Revenue -0.0191∗∗∗ -0.0222∗∗∗ -0.0209∗∗∗ -0.0201∗∗∗ -0.0200∗∗∗

(0.00574) (0.00660) (0.00686) (0.00700) (0.00698)Battlefield Losses 0.0456∗∗ 0.0486∗∗ 0.0485∗∗ 0.0486∗∗

(0.0230) (0.0211) (0.0207) (0.0207)

Model ParametersFighting Season (FS) Fixed Effect Yes Yes Yes Yes YesFS Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesFS Combat Operations (all, levels) Yes Yes Yes Yes YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.496 0.501 0.504 0.506 0.506

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Fighting season parametersare notated with the abbreviation FS. Battlefield losses in our sample have a mean of 4.605 andstandard deviation of 10.547. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

52

Table 10: Effects of rebel capacity and government surveillance missions on within-dayrandomization of indirect fire attacks

(1) (2) (3) (4) (5)Opium Revenue -0.0191∗∗∗ -0.0203∗∗∗ -0.0190∗∗∗ -0.0181∗∗∗ -0.0181∗∗∗

(0.00574) (0.00601) (0.00623) (0.00646) (0.00644)Government Surveillance Operations 0.0916∗∗∗ 0.0917∗∗∗ 0.0932∗∗∗ 0.0930∗∗∗

(0.0209) (0.0215) (0.0210) (0.0211)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesFS Combat Operations (all, levels) Yes Yes Yes Yes YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.496 0.501 0.504 0.506 0.506

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Fighting season parameters arenotated with the abbreviation FS. Government Surveillance in our sample have a mean of .425and standard deviation of 3.22. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

Table 11: Impact of within-day randomization of indirect fire attacks on ‘find and clear’missions

(1) (2) (3) (4)Randomization Parameter 0.698∗∗∗ 0.689∗∗∗ 0.683∗∗∗ 0.680∗∗∗

(0.260) (0.256) (0.255) (0.253)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesIED Deployment (levels) Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.941 0.942 0.942 0.942

Notes: Outcome of interest is ‘find and clear’ missions (levels). Quantityof interest is the (log) p-value of the randomness test. All regressions in-clude fighting season fixed effects. All regressions partial out total bombdeployment (levels). Column 2-4 add controls for the intensive margin offighting during the fighting, harvest, and planting seasons respectively. Het-eroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

53

Table 12: Impact of within-day randomization of indirect fire attacks on bomb-inducedcasualties

(1) (2) (3) (4)Randomization Parameter -0.182∗ -0.177∗ -0.175∗ -0.173∗

(0.101) (0.0992) (0.101) (0.100)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesIED Deployment (levels) Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.853 0.854 0.854 0.854

Notes: Outcome of interest is bomb-induced casualties (levels). Quantityof interest is the (log) p-value of the randomness test. All regressions in-clude fighting season fixed effects. All regressions partial out total bombdeployment (levels). Column 2-4 add controls for the intensive margin offighting during the fighting, harvest, and planting seasons respectively.Heteroskedasticity robust standard errors clustered by district are re-ported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, *p < 0.1.

54

Table 13: Heterogeneous effects of rebel capacity on within-day randomization of indirectfire attacks with respect to variation in reservation wages (via informal taxation by corruptofficials)

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0177∗∗ -0.0269∗∗∗ -0.0268∗∗∗ -0.0270∗∗∗

(0.0137) (0.00688) (0.00745) (0.00750) (0.00740)Corruptible Officials -0.215 -0.676∗ -0.669 -0.681∗

(0.358) (0.390) (0.405) (0.405)Corruptible × Revenue -0.0430∗∗∗ -0.0329∗∗ -0.0291∗∗ -0.0288∗∗

(0.0152) (0.0133) (0.0125) (0.0124)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.164 0.182 0.196 0.196

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

55

Table 14: Heterogeneous effects of rebel capacity on within-day randomization of indirectfire attacks with respect to variation in income volatility

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0583∗∗∗ -0.0588∗∗∗ -0.0550∗∗∗ -0.0551∗∗∗

(0.0137) (0.0146) (0.0143) (0.0121) (0.0121)High Revenue Volatility -0.890∗ -0.851∗ -0.864∗ -0.866∗

(0.495) (0.477) (0.489) (0.488)High Revenue Volatility × Revenue -0.00215 -0.00253 -0.00210 -0.00198

(0.0336) (0.0324) (0.0340) (0.0343)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.164 0.180 0.196 0.196

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasons re-spectively. Additional parameters are noted in the table footer. Heteroskedasticity robust standarderrors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, *p < 0.1.

56

APPENDIX [FOR ONLINE PUBLICATION ONLY]

List of Figures and Tables

Table/figure numbers are noted in left column. Page numbers are noted in the right column.

Supplemental Figures

A-1 Estimated first stage effects of agronomic inputs on opium revenue. . . . . . A-34A-2 Bivariate relationship between opium revenue and p-value of randomization

test of combat (direct fire attacks) in Afghanistan . . . . . . . . . . . . . . . A-42A-3 Bivariate relationship between opium revenue and p-value of randomization

test of combat (IED attacks) in Afghanistan . . . . . . . . . . . . . . . . . . A-42

Supplemental Tables

A-1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-12A-2 Impact of rebel capacity on spatial clustering of indirect fire attacks . . . . . A-14A-3 Impact of rebel capacity on within-day randomization of indirect fire attacks,

accounting for state capacity measures (part i) . . . . . . . . . . . . . . . . . A-16A-4 Impact of rebel capacity on within-day randomization of indirect fire attacks,

accounting for state capacity measures (part ii) . . . . . . . . . . . . . . . . A-17A-5 Impact of rebel capacity on within-day randomization of indirect fire attacks,

accounting for rebel intimidation tactics . . . . . . . . . . . . . . . . . . . . A-18A-6 Estimating treatment effect bounds using the Oster coefficient stability test . A-19A-7 Heterogeneous effects of rebel capacity on within-day randomization of indi-

rect fire attacks with respect to historical territorial control by Taliban . . . A-20A-8 Reduced form effects of rebel capacity on production of indirect fire attacks . A-21A-9 Second stage effects of rebel capacity on production of indirect fire attacks . A-22A-10 Impact of rebel capacity on within-day randomization of indirect fire attacks,

excluding non-producers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-23A-11 Impact of rebel capacity on within-day randomization of indirect fire attacks,

adjusting measure of revenue . . . . . . . . . . . . . . . . . . . . . . . . . . . A-24A-12 Impact of rebel capacity on within-day randomization of indirect fire attacks,

instrumental variables approach (second stage), accounting for aid delivery . A-25A-13 Impact of suitability instrument on opium revenue, instrumental variables

approach (first stage, main estimating sample) . . . . . . . . . . . . . . . . . A-26A-14 Impact of suitability instrument on opium revenue, instrumental variables

approach (first stage, full panel sample) . . . . . . . . . . . . . . . . . . . . . A-27

A-1

A-15 Impact of suitability instrument on within-day randomization of indirect fireattacks, instrumental variables approach (reduced form, main estimating sam-ple) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-28

A-16 Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, main estimating sample) accounting for potential variationin instrument compliance via irrigation mechanism . . . . . . . . . . . . . . A-29

A-17 Impact of suitability instrument on opium revenue, instrumental variablesapproach (first stage, full panel sample) accounting for potential variation ininstrument compliance via irrigation mechanism . . . . . . . . . . . . . . . . A-30

A-18 Impact of suitability instrument on opium revenue, instrumental variablesapproach (first stage, main sample, LASSO selection) . . . . . . . . . . . . . A-31

A-19 Impact of suitability instrument on opium revenue, instrumental variablesapproach (first stage, full panel sample, LASSO selection) . . . . . . . . . . . A-32

A-20 Impact of suitability instrument on within-day randomization of indirect fireattacks, instrumental variables approach (reduced form, main sample, LASSOselection) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-33

A-21 Impact of agronomic instruments on opium revenue, instrumental variablesapproach (first stage, main sample, multiple IV approach) . . . . . . . . . . A-35

A-22 Impact of agronomic instruments on opium revenue, instrumental variablesapproach (first stage, full panel sample, multiple IV approach) . . . . . . . . A-36

A-23 Impact of agronomic instruments on within-day randomization of indirectfire attacks, instrumental variables approach (reduced form, main sample,multiple IV approach) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-37

A-24 Heterogeneous effects of rebel capacity on within-day randomization of indi-rect fire attacks with respect to potential intelligence gathering via securitybase breaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-38

A-25 Heterogeneous effects of rebel capacity on within-day randomization of indi-rect fire attacks with respect to potential intelligence gathering via insiderattacks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-39

A-26 Effects of rebel capacity and battlefield losses on within-day randomization ofindirect fire attacks, accounting for counterinsurgent operations from TablesA-3 and A-4] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-40

A-27 Impact of rebel capacity on within-day randomization of direct fire attacks . A-43A-28 Impact of rebel capacity on within-day randomization of IED attacks . . . . A-44

A-2

A1 Theory

Proof of Proposition 1

For event H, the complement is denoted H ′. We introduce auxiliary random variables Ti, Sitaking two values 0 and 1; Ti = 1 means that i-th time slot is defended, Ti = 0 means thatthere is no defense at time i; Si = 1 means that the test of time slot i shows it as defended,and Si = 0 means that the slot i tests as vulnerable. In the absense of index i, S and Tcorrespond to any time slot.

Recall that P (S|T ) = P (S ′|T ′) = θ.33 Finally, let C denote the event that attack issuccessful during a time slot with an attack. We assume that P (C|T ′) = p and P (C|T ) = 0.

Recall that, the parameters are: n is the number of time slots, r is the number of defensesallocated by the government, and a is the number of attacks. The optimal strategy for thegovernment is to allocate r defenses uniformly over n time windows. Then for each windowt(r) = P (time slot is protected)= r

n.

We will show that for rebels the optimal strategy looks as follows. If a < x, the attacksare allocated uniformly at random among the vulnerable time slots. If a > x then there isa threshold value, a function of parameters of the model and x, that determines how manymore put in the vulnerable time windows; above that, they start to put into the windowsthat tested “defended”, again uniformly.

First, observe that cases x = 0 and x = n are trivial: there is no information to infer, sothe optimal strategy for rebels is to allocate attacks uniformly across n time slots. In whatfollows, we will assume that 0 < x < n.

After n slots are tested, a (vector) signal s = (s1, .., sn) is obtained and value N = x, thenumber of slots that tested vulnerable is produced. In other words, a (random) partition ofa set J into two sets, J−(x) - slots tested vulnerable, and its complement J+(x), is obtained.Define N1 = |J−(x)∩L|, the number of defended sites that tested vulnerable, i.e., the numberof “false positives”; and N2 = |J−(x) ∩ U |, the number of correct vulnerable signals. Thetotal number of sites that tested vulnerable is N ≡ Nn,r = N1 +N2.

N1 and N2 are independent binomial random variables. Denote pi(j) the p.m.f. ofNi, i = 1, 2, and p(j|l, p), j = 0, 1, ..., l – the p.m.f. of a binomial random variable with ltrials and probability of success p. Then p1(j) = p(j|r, 1− θ) and p2(j) = p(j|n− r, θ).

Now the p.m.f. of N , gn,r(x), 0 ≤ x ≤ n, can be calculated by the standard discreteconvolution formula.

gn,r(x) =∑

0≤j≤r, 0≤x−j≤n−r

p1(j)p2(x− j).

33All the results go through with the arbitrary parameters α = P (S|T ), β = P (S′|T ′) subject to α+β > 1,i.e., that the test is informative. A standard interpretation for α and β as α = P (positive test|disease) =sensitivity; and β = P (negative test|no disease)= specificity, two important characteristics of any statisticaltest.

A-3

We start with the following basic equations:

P (Ci = 1|Ti = 1) = 0,

P (Ci = 1|Ti = 0, ui) = p(ui),

where ui is the number of attacks launched against target i, and p(u) is the success function,the probability of at least one successful attack on a target which faces u attacks.

As we assumed that the success is independent across attacks, p(u) = 1− (1− p)u. Thefunction p(u) is increasing and upward concave, and the function ∆p(u) ≡ p(u + 1) − p(u)is decreasing. The diminishing effect of each extra attack will play an important role indeterming the optimal strategy.

We start with a straightforward lemma.

Lemma A1 The posterior probability of signal distribution is uniform conditional on thenumber of signals “vulnerable” x :

P (s1, ..., sn) = P (N = x)/

(n

x

). (A1)

The posterior probability that target i is vulnerable conditional on the full vector signal(s1, ..., sn) is equal to the conditional probability that target i is vulnerable conditional onlyon the individual signal si and the total number of “vulnerable” signals x.

P (Ti = 0|s1, ..., sn) = P (Ti = 0|si, N = x). (A2)

Proof. (A1) is straightforward. The left side of formula (A2) can be written as

P (Ti = 0)P (s|Ti = 0)/P (s) = P (si|Ti = 0)P (s−i|Ti = 0)/P (s),

where s−i is vector s without coordinate si. Using (A1), we can replace P (s) = P (N =x)/(nx

). The right side of formula (A2) can be written as

P (Ti = 0, si, N = x)

P (si, N = x)=P (Ti = 0)P (si|Ti = 0)P (N = x|si, Ti = 0)

P (N = x)P (si|N = x).

Let si = 0. Then, on the left-hand side, using (A1) for a problem with n− 1 targets andk attacks, we have

P (s−i|Ti = 0) = Pn−1,k(N = x− 1)/

(n− 1

x− 1

).

In the right-hand side we have P (si|N = x) = x/n and

P (N = x|si = 0, Ti = 0) = Pn−1,k(N = x− 1).

Finally, since(nx

)=(n−1x−1

)n/x, we obtain that after all reductions the left and the right sides

of formula (A2) coincide. The proof for the case si = 1 is similar.

A-4

The formula (A2) is at the heart of the intuition behind our main results. The optimalstrategy π(·|x) of the attacker depends on function p(u) and on the ratio ρ(x|θ), reflectingthe relative vulnerability of targets with s = 0 and s = 1, which, in turns, depends onparameters n, r and θ.

The next Lemma critical ratio that determines the threshold a(x) for each x is definedby the following equation:

ρn,r(x) = ρn,r(x|θ) ≡p−(x)

p+(x).

Our next goal is to establish that ρn,r(x) ≥ 1.

Lemma A2 (a) The probabilities p−(x) ≡ P (T ′|S ′, x) and p+(x) ≡ P (T ′|S, x)) for 0 < x <n are given by formulas

p−(x) =r

x∗ θ ∗ gn−1,r(x− 1)

gn,r(x),

p+(x) =r

n− x∗ (1− θ) ∗ gn−1,r(x)

gn,r(x).

(b) The ratio ρn,r(x|θ), 0 < x < n, is given by the formula

ρn,r(x|θ) =θ

1− θn− xx

gn−1,r(x− 1)

gn−1,r(x). (A3)

Proof. (a) For the sake of brevity, we denote P (·|N = x) ≡ P (·|x) and event D(x) = (N =x) = D. By definition p−(x) ≡ P (T ′|S ′, x) = P (T ′S ′, x)/P (S ′, x), and p+(x) ≡ P (T ′|S, x) =P (T ′S, x)/P (S, x). We have

P (T ′S ′D) = P (T ′)P (S ′D|T ′) = P (T ′)P (S ′|T ′)P (D|T ′S ′),P (T ′SD) = P (T ′)P (SD|T ′) = P (T ′)P (S|T ′)P (D|T ′S). (A4)

We also have P (T ′) = rn, P (S ′|T ′) = θ, and P (S|T ′) = 1− θ. Therefore, to prove the result,

it is sufficient to show that

P (D|T ′S ′) = gn−1,r(x− 1),

P (D|T ′S) = gn−1,r(x),

P (S ′D) = gn,r(x) ∗ xn,

P (SD) = gn,r(x) ∗ n− xn

.

To show that P (D|T ′S ′) = gn−1,r(x − 1), observe that if N = x, and a particular slot hasno defense, T ′, and produced vulnerable signal, S ′, then in the remaining n − 1 slots thereare r defenses with x− 1 vulnerable signals. Similarly, to show that P (D|T ′S) = gn−1,r(x),observe that if N = x, and a particular slot has no defense, T ′, and produced “defended”

A-5

signal, S, then in the remaining n−1 slots there are r defenses with x vulnerable signals. Todemonstrate that P (S ′D) = gn,r(x) ∗ x

n, note that P (S ′D) = P (D)P (S ′|D), P (D) = gn,r(x)

and P (S ′|D) = xn, the probability for one vulnerable signal among x to be in a particular

slot. Similarly, P (SD) = P (D)P (S|D), and P (S|D) = n−xn

, the probability for one defendedsignal among n− x to be in a particular slot.

(b) is a straightforward corollary to (a).

Lemma A3 34

(a) ρ(x) > 1.(b) Functions ρn,n−1(x) = θ2

1−θ2 for all x, while functions ρn,r(x|θ) for r < n − 1 aremonotonically increasing in x for 0 < x < n.

(c) Functions ρn,r(x|θ) are monotonically decreasing for all fixed r, 0 < x < n when n isincreasing.

Proof. (a) Let Dn,r be a sum of n Bernoulli random variables, r of which have parameter1− θ, and n− r of which have parameter θ > 1− θ, 0 ≤ r ≤ n. Let

gn,r(x) = P (Dn,r = x), 0 ≤ x ≤ n;

fn,r(x) =gn,r(x− 1)

gn,r(x), 1 ≤ x ≤ n;

ρn,r(x) =n+ 1− x

x

θ

1− θfn,r(x), 1 ≤ x ≤ n.

We assume also that fn,r(0) = ρn,r(0) = 0.

Denote c = θ2

1−θ2 . Then θ > 12

implies c > 1.It is easy to check that

ρn,0(x) = 1, for 1 ≤ x ≤ n ;

ρn,n(x) = c, for 1 ≤ x ≤ n ; (A5)

ρn,r(n) =rc+ n− r

n= 1 +

r

n(c− 1) for 0 ≤ r ≤ n .

Using the total probability formula, we obtain a recursive relationship:

fn,r(x) =gn,r(x− 1)

gn,r(x)=

(1− θ)gn−1,r(x− 1) + θgn−1,r(x− 2)

(1− θ)gn−1,r(x) + θgn−1,r(x− 1)

=1− θ + θfn−1,r(x− 1)

1−θfn−1,r(x)

+ θfor 1 ≤ r, x ≤ n− 1 . (A6)

34We thank Isaac Sonin and Ernst Presman for their help with proving this lemma.

A-6

This implies that

ρn,r(x) =n− x+ 1

x

θ

1− θ1− θ + θ x−1

n−x+11−θθρn−1,r

(x− 1)

1−θρn−1,r(x)

n−xx

1−θθ

+ θ

=n− x+ 1 + (x− 1)ρn−1,r(x− 1)

n−xρn−1,r(x)

+ xfor 1 ≤ r, x ≤ n− 1 . (A7)

(A5) is the induction base. By induction, the numerator in (A7) is strictly increasing, andthe denominator is strictly decreasing, and hence the right side in (A7) is strictly increasingand depends only on c. When c grows from 1 to ∞ (that is, θ is increasing from 0 to 1

2), it

is strictly increasing from 1.

(b) Now we can show that for fixed n ≥ 2, 1 ≤ r ≤ n − 1, c > 1, function ρn,r(x) isstrictly increasing in x.

Again, we use induction by n. Let ρ(x) = ρn−1,r(x), H(x) = n − x + xρ(x). Then, by(A7),

ρn,r(x) = ρ(x)H(x− 1)

H(x), ρn,r(x+ 1)− ρn,r(x) =

C(x)

H(x+ 1)H(x),

where

C(x) = ρ(x+ 1)H2(x)− ρ(x)H(x+ 1)H(x− 1)

= ρ(x+ 1)[(n− x)2 + 2x(n− x)ρ(x) + x2ρ2(x)

]= −ρ(x)[n− x− 1 + (x+ 1)ρ(x+ 1)] [n− x+ 1 + (x− 1)ρ(x− 1)]

= ρ(x+ 1)[(n− x)2 + 2x(n− x)ρ(x) + x2ρ2(x)

].

We can check, using (A6) and (A7), that

ρ2,1(2) =1 + c

2> ρ2,1(1) =

2c

1 + c,

ρ3,1(3) =2 + c

3> ρ3,1(2) =

1 + 2c

2 + c> ρ3,1(1) =

3c

1 + 2c,

ρ3,2(3) =1 + 2c

3> ρ3,2(2) = c

2 + c

1 + 2c> ρ3,2(1) =

3c

2 + c,

and hence the proof is complete for n = 2 and n = 3.For n ≥ 4 and 2 ≤ x ≤ n− 2, we have x(n−x)−n ≥ 0, and by induction, it follows that

C(x) > ρ(x)+ρ2(x)ρ(x+1)−ρ(x)ρ(x+1)− ρ2(x)

= ρ(x)(ρ(x+ 1)− 1)(ρ(x)− 1) > 0

for 2 ≤ x ≤ n− 2.

A-7

To prove (c), it remains to show that ρn−r,r(2)− ρn−r,r(1) > 0 and ρn−r,r(n)− ρn−r,r(n−1) > 0. Using the total probability formula,

ρn,r(n− 1) =2

n− 1

θ

1− θP (Dnr = n− 2)

P (Dnr = n− 1)

=1

n− 1

(n− r)(n− r − 1) + 2(n− r)rc+ r(r − 1)c2

n− r + cr. (A8)

Then, using (A6), we obtain

ρn,r(n)− ρn,r(n− 1) =(n− r)r(c− 1)2

n(n− 1)(n− r + cr)> 0 .

Similarly,

ρn,r(2) =(n− 1)(c(n− r) + r)

c2(n− r)(n− r − 1) + 2(n− r)rc+ r(r − 1),

ρn,r(1) =nc

r + c(1− r),

ρn,r(2)− ρn,r(1) =(n− r)r(c− 1)2

[c2(n− r)(n− r − 1) + 2(n− r)rc+ r(r − 1)](r + c(1− r)).

Let B−(s) = {i : si = 0} and B+(s) = {i : si = 1}. Then, using (A2), we obtain that,given a strategy π = (u1, ..., un) and any signal s with N(s) = x, the expected value of astrategy π is

w(π|x) = 1− Πnj=1(1− P (Cj|uj, sj, x)).

Let U− ≡ U−(π|s) = {uj, j ∈ B−(s)} and U+ ≡ U+(π|s) = {uj ∈ B+(s)} be two possiblesets of the values of uj at vulnerable and non-vulnerable targets. Formula (A2) immediatelyimplies that all strategies obtained by permutations of sets (U−, U+) among correspondingtargets have the same value.

We prove later that the upward concavity of function p(u) implies that the optimalstrategy has the property that the number of attacks against any pair of targets with thesame signal is the same or almost the same: as the number of attacks is integer, there mightbe a difference of one attack between two targets with the same signals. Let us assume forsimplicity that both equalities hold: ui = u−, i ∈ B−(s) and ui = u+, i ∈ B+(s).

Let us do the following transformation:

ln (1− w(π|x)) =n∑j=1

(1− P (Ti = 0|si, x)p(ui))

= n−n∑j=1

P (Ti = 0|si, x)p(ui)

= n− p−(x)∑

i∈B−(s)

p(ui)− p+(x)∑

i∈B+(s)

p(ui).

A-8

Now, the same strategy π that maximizes the function v(π|x) = p−(x)∑

i∈B−(s) p(ui) −p+(x)

∑i∈B+(s) p(ui) is maximizing the strategy value (π|x).

The following lemma concludes the proof of Proposition 1. To obtain the optimal strategy,we use the necessary equilibrium condition: with an optimal allocation it is impossible toincrease the payoff by moving an attack from one target to another. Given N = x, 0 ≤ x ≤ nthe allocation of attacks depends on the number a of attacks available. The optimal strategyhas the following structure. Initially, all attacks are launched one by one into each of xvulnerable slots until the threshold level

d(x) = mini≥1

{i|ρ(x|θ) (1− p)i < 1

}(A9)

is reached in each of them or the attack resources are exhausted. Afterwards, the attacksare added one by one to non-vulnerable slot until there is an attack on each of them. Then,attacks are added one by one until each of the vulnerable slots has d(x) + 1 attacks on eachof them, then back to non-vulnerable slots until each has at least 2 attacks, etc. This “filland switch” process stops when the attacker runs run out of resources. If x = 0 or n thenjust all slots are filled sequentially. The outcome of this process will be an allocation inwhich either all “vulnerable” slots will have the same number of attacks launched againstthem, or all “not vulnerable” slots, or both. If all “not vulnerable” slots have no attacksallocated to them, then the number of attacks against each “vulnerable” slot does not exceedd(x). (Trivially, after the process is complete, the attacker will have to uniformly randomizethe distributions of attacks over sets of slots with the same sign: otherwise, the uniformdistribution of protection by the defender would not be a best response.) The threshold a(x)in the statement of Proposition 1 is a function of both x (via d(x)) and the total number ofattacks available, a.

Lemma A4 (i) Let π(x) = (ui, i = 1, 2, ..., n) be an optimal strategy . Then |ui1 − ui2| ≤ 1when the signals at time slots i1, i2 have the same sign.

(ii) Let π(x) = (ui, i = 1, 2, ..., n) be a strategy, 0 < x < n, u− be the number of attacksin some vulnerable slot, u+ be the number of attacks in some protected slot, and d = d(x) isdefined by formula (A9). Then, if u−−u+ > d(x) or, if u+ ≥ 1 and u−−u+ < d(x)−1, thenstrategy π is not optimal, or, equivalently, if π is optimal, and u+ = 0, then 1 ≤ u− ≤ d(x),and if u+ ≥ 1, then u− − u+ = d(x) or d(x)− 1.

Proof. (i) Let J be a subset of slots, and recall that Cj = 1 when slot j is destroyed. Theconditional independence of testing and attacks’s successes, and total probability formulaimply the following formula for the conditional probability of the destruction of a particularslot with u ≥ 1 attacks

P (C|u, F ) = P (C|u, T = 0)P (T = 0|F ) = p(u)P (T = 0|F ),

where F is any event generated by testing (signals).

A-9

Using the above formula and the definitions of ρ(x), p−(x) and p+(x), we have:

P (C|u, S = 1, x) = P (T = 0|S = 1, x)P (C|u, T = 0) = p+(x)p(u),

P (C|u, S = 0, x) = P (T = 0|S = 0, x)P (C|u, T = 0) = p−(x)p(u) = ρ(x)p+(x)p(u).(A10)

Suppose that the statement is not true and let us say ui1 = u, ui2 = j, u − j ≥ 2 andSi1 = Si2 = 1. The concavity of function p(·) implies that p(u+ 1) + p(j − 1) > p(u) + p(j).Then, using the formulas in (A10), we have

P (C = 1|u+ 1, S = 1, x) + P (C|j − 1, S = 1, x) = p+(x)[p(u+ 1) + p(j − 1))] >

> p+(x)[p(u) + p(j)] = P (C|u, S = 1, x) + P (C|j, S = 1, x). (A11)

Thus, v(π|x) is not maximized and our initial strategy is not optimal. The proof for Si1 =Si2 = 0 is similar with p+(x) replaced by p−(x) = ρ(x)p+(x).

(ii) Let d(x) = d. We will show that if u− − u+ > d for some pair of vulnerable andprotected slots, then a transfer of one attack from a vulnerable slot from this pair to aprotected slot will increase the value of a strategy . Similarly, if u+ ≥ 1 and u−−u+ < d− 1for such pair, then the inverse transfer will increase the value. As always, we assume thata+b > 1 and then ρ(x) > 1 for 0 < x < n, and hence u− ≥ u+. Let u− = u, u+ = j, P (·|N =x) = P (·|x), and denote the incremental utilities for vulnerable and protected slots as

∆C−(u|x) = P (C|u+ 1, S ′, x)− P (C|u, S ′+(j|x) = P (C|j + 1, S, x)− P (C|j, S, x).

Then, formula (A10) implies that their difference for 0 ≤ j ≤ i is

∆(u, j|x) = ∆C−(u|x)−∆C+(j|x)

= p (1− p)u ρ(x)p+(x)− p (1− p)j p+(x))

= p (1− p)j p+(x)[ρ(x) (1− p)u−j − 1].

The definition of d = d(x) in (A9) implies that ∆(u, j|x) is positive if j = 0, u < d, or ifj ≥ 1, u− j < d. Similarly, ∆(u, j|x) is negative if j = 0, u ≥ d, or if j ≥ 1, u− j ≥ d. Theseinequalities imply the claim. Also, note that if p = 1, then d(x) = 1 for all 0 < x < n, andif p is decreasing to zero, then d(x) tends to infinity.

This concludes the proof of Proposition 1. �

Proof of Proposition 2

By (A7) in the proof of Lemma A3, the critical ratio ρn,r(x|θ) is given by the recursiveformula

ρn,r(x) =n− x+ 1 + (x− 1)ρn−1,r(x− 1)

n−xρn−1,r(x)

+ xfor 1 ≤ r, x ≤ n− 1 .

For each r, one can use the above formula and induction on n to show that ρn,r(x|θ) is anincreasing function of θ for each x, x ≤ n− 1. Indeed, ρn,r(x|θ) is monotonically increasingin ρn−1,r(x|θ). Then, the induction step completes the argument.

A-10

Now, take any θ1, θ2 such that θ1 < θ2. As ρn,r(x|θ1) < ρn,r(x|θ2)), for the thresholdsd(x|θ1) and d(x|θ2) defined by (A9), one has d(x|θ1) ≤ d(x|θ2). This means that attacks aremore temporally concentrated with θ2 than with θ1, i.e., a(x|θ1) ≤ a(x|θ2). �

Proof of Proposition 3

Observe that ρn,r(x) does not depend on p. By (A9), d(x) = mini≥1

{i|ρ(x|θ) (1− p)i < 1

}.

When p increases, d(x) goes down, which results in less temporal clustering of attacks.Similarly, when r increases, so does ρn,r(x) by (A6) and (A7), which results in a higher d(x),and more temporally clustered attacks. �

A-11

A2 Empirical Appendix

In this brief empirical appendix, we introduce supplemental results.

A2.1 Descriptive Statistics

Table A-1: Summary statistics

Variable Mean Std. Dev. Min. Max. NOutcome of InterestIndirect fire, likelihood parameter -7.025 3.918 -39.686 0 600Rebel CapacityOpium revenue 20.506 25.403 0 75.518 600Opium revenue, regional yield/prices 20.017 24.7 0 73.587 600Trends in ViolenceIndirect fire trend, fighting season 19.187 21.153 5 253 600Indirect fire trend, growing/harvest season 10.788 15.194 0 161 600Indirect fire trend, planting season 7.663 10.925 0 109 600

Notes: summary statistics are calculated for the sample studied in the main estimatingequation.

A-12

A2.2 Spatial Clustering of Attacks

In this subsection we detail a preliminary test of spatial clustering in attack patterns.The central inferential challenge for studying spatial dynamics is identifying the set of

counterfactual locations that could have been attacked but were not. If, for example, theset of locations that could be targeted was a known quantity and did not change over time,it would be possible to identify clustering among the finite set of targets. In Afghanistan,this quantity is unknown and even it were recoverable from the highly classified Blue ForceTracker database, the number of potential targets and their location is endogenous to conflictdynamics. Investigations of temporal clustering have the distinct advantage of a finite andclearly defined set of potential attack slots.

As a preliminary attempt to address this question regarding spatial clustering, we developa 5 kilometer × 5 kilometer grid of Afghanistan. We link all observed combat activity bytype to this grid. To identify relevant elements of the grid, we restrict our analysis only togrid cells that see some recorded activity during the entire conflict (extensive margin). Thisgrid selection rule indicates that at some point during the war, there was a relevant targetpresent within this cell (which or may not have been a target of prior or later operations).To reduce potential concerns about endogenous changes in the location of targets due tospatial attack patterns, we keep this grid sample fixed over time. We then calculate an Indexof Dispersion for each district-fighting season by linking grid cells to their correspondingparent administrative unit (Perry and Mead, 1979). This type of index is common in thestudy of spatial point processes (eg, seedling dispersion).

Consistent with the main analysis on timing, we restrict our study of spatial dynamics tounit-years with at least five combat events. Low values of the index indicate uniformity inthe spatial allocation of attacks across relevant cells; higher values indicate that the spatialpattern was highly unlikely to have occurred by random chance and exhibits characteristicsof uneven density (ie, spatial clustering of attacks). Given the flipped interpretation of theoutcome variable, we expect a positive correlation with revenue if our model extends tospatial allocation of attacks as well as temporal clustering.

We replicate our benchmark specification in Table A-2. Notice that spatial clustering isincreasing in revenue. Substantively, a one standard deviation increase in revenue increasesthe intensive margin of spatial clustering by .2 standard deviations.

A-13

Table A-2: Impact of rebel capacity on spatial clustering of indirect fire attacks

(1) (2) (3) (4)Opium Revenue 23.31∗∗ 25.42∗∗∗ 21.37∗∗∗ 22.14∗∗∗

(9.256) (8.144) (6.361) (6.238)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 620 620 620 620No. of Clusters 158 158 158 158R2 0.0683 0.397 0.419 0.441

Notes: Outcome of interest is the index of dispersion. Higher values suggesta given spatial pattern is highly unlikely to have occurred by random chanceand exhibits uneven spatial density (clustering). The quantity of interestis opium revenue for a given district-year. All regressions include fightingseason fixed effects. Column 2-4 add controls for the intensive margin offighting during the fighting, harvest, and planting seasons respectively. Het-eroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-14

A2.3 Additional Threats to Inference

In this subsection we detail additional potential threats to inference.It is possible that revenue from opium production may attract additional counterinsurgent

investments. Consistent with our theoretical model, to defeat rebels accumulating resources,security forces may have deployed additional resources that could complicate estimationof the effect of rebel capacity on the randomness of combat. We focus on six measures ofcounterinsurgent capacity: close air support missions, cache discoveries, IED neutralizations,detention of insurgent forces, counterinsurgent surveillance operations, and safe house raidsyielding actionable intelligence assets (salary and recruitment logs, hard drives, forensicmaterials, etc.). We sequentially add these covariates to Equation 1. We present these resultsin Tables A-3 and A-4. For comparison, the most conservative specification from Table 1(Column 4) is included as Column 1 in both of these tables. Notice that these measuresof counterinsurgent capacity improve the explanatory power of our models, although themagnitude of the main effect is slightly attenuated.

A-15

Table A-3: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for state capacity measures (part i)

(1) (2) (3) (4)Opium Revenue -0.0549∗∗∗ -0.0420∗∗∗ -0.0346∗∗∗ -0.0274∗∗∗

(0.0125) (0.00989) (0.00785) (0.00945)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes YesAdditional ParametersWeapon Caches Cleared No Yes No NoClose Air Support No No Yes NoIEDs Cleared No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.187 0.243 0.299 0.320

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fightingseason fixed effects as well as controls for the intensive margin of fighting duringthe fighting, harvest, and planting seasons respectively. Additional parameters arenoted in the table footer. Heteroskedasticity robust standard errors clustered bydistrict are reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, *p < 0.1.

A-16

Table A-4: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for state capacity measures (part ii)

(1) (2) (3) (4)Opium Revenue -0.0549∗∗∗ -0.0539∗∗∗ -0.0528∗∗∗ -0.0477∗∗∗

(0.0125) (0.0120) (0.0116) (0.0103)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes YesAdditional ParametersCoalition Surveillance No Yes No NoSafe House Raids No No Yes NoDetention of Susp. INS No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.187 0.188 0.193 0.221

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fightingseason fixed effects as well as controls for the intensive margin of fighting duringthe fighting, harvest, and planting seasons respectively. Additional parameters arenoted in the table footer. Heteroskedasticity robust standard errors clustered bydistrict are reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, *p < 0.1.

A-17

Opium production might also be influenced by coercive tactics used by the Taliban tointimidate civilians. In general, these tactics are difficult to track. These coercive tacticsrepresent a problematic omitted variable if they are indeed correlated with production andfurther correlated with the sophistication of combat tactics used during the fighting sea-son. These are plausible concerns. To address them, we incorporate additional informationfrom our military records which tracks attempts to intimidate the civilian population, usingmethods like ‘night letters’ and shows of non-lethal force as well as deliberate killings ofgovernment collaborators (like informants and security force recruits). Our main effect isonly slightly attenuated when we account for these rebel intimidation tactics in Columns 2and 3 of Table A-5.

Table A-5: Impact of rebel capacity on within-day randomization of indirect fire attacks,accounting for rebel intimidation tactics

(1) (2) (3)Opium Revenue -0.0549∗∗∗ -0.0492∗∗∗ -0.0484∗∗∗

(0.0125) (0.0121) (0.0104)

Model ParametersFighting Season Fixed Effect Yes Yes YesFighting Season Activity (levels) Yes Yes YesGrowing Season Activity (levels) Yes Yes YesPlanting Season Activity (levels) Yes Yes YesAdditional ParametersTaliban Intimidation No Yes NoCollaborator Killings No No YesModel StatisticsNo. of Observations 600 600 600No. of Clusters 154 154 154R2 0.187 0.204 0.227

Notes: Outcome of interest is the (log) p-value of the randomness test.The quantity of interest is opium revenue for a given district-year. Allregressions include fighting season fixed effects as well as controls forthe intensive margin of fighting during the fighting, harvest, and plant-ing seasons respectively. Additional parameters are noted in the tablefooter. Heteroskedasticity robust standard errors clustered by districtare reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05,* p < 0.1.

A-18

Table A-6: Estimating treatment effect bounds using the Oster coefficient stability test

Panel A: Baseline Regression Diagnostic Information(1) (2)

Treatment Outcome Baseline effect Controlled effectVariable Variable (Std. error), [R2] (Std. error), [R2]Opium revenue Temporal clustering -0.0552*** (.0125) [0.128] -.0246*** (.0081) [0.374]

Panel B: Oster Coefficient Stability Test Results(3) (4)

Treatment Outcome Effect for Rmax Alt. Effect for Rmax

Variable Variable ((βRmax- βctrl)

2) [Rmax] ((βRmax- βctrl)

2) [Rmax]Opium revenue Temporal clustering -0.007 (.0003) [.486] -0.232 (.0431) [.486]

Notes: Bounds for treatment effects are estimated using the Oster coefficient stability test(Oster, 2017). Unobservables are assumed to have as much explanatory power as the observ-ables. Rmax set at 1.3 (the threshold suggested in (Oster, 2017)). Model specifications aredrawn from least and most conservative main specifications. *** p < 0.01, ** p < 0.05, *p < 0.1.

A-19

Table A-7: Heterogeneous effects of rebel capacity on within-day randomization of indirectfire attacks with respect to historical territorial control by Taliban

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0258∗∗∗ -0.0288∗∗∗ -0.0232∗∗ -0.0231∗∗

(0.0137) (0.00936) (0.00995) (0.00994) (0.00985)Historical Taliban Control -0.0634 0.0974 0.109 0.111

(0.401) (0.404) (0.406) (0.407)Hist. Control × Revenue -0.0328∗∗∗ -0.0307∗∗∗ -0.0325∗∗∗ -0.0325∗∗∗

(0.0120) (0.0116) (0.0121) (0.0120)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.156 0.172 0.188 0.188

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-20

Table A-8: Reduced form effects of rebel capacity on production of indirect fire attacks

(1) (2) (3)Suitability × Agg. Production 0.135∗∗∗ 0.0938∗∗∗ 0.0903∗∗

(0.0360) (0.0338) (0.0352)

Model ParametersFighting Season Fixed Effect Yes Yes YesFighting Season Activity (levels) Yes Yes YesGrowing Season Activity (levels) No Yes YesPlanting Season Activity (levels) No No YesModel StatisticsNo. of Observations 3582 3582 3582No. of Clusters 398 398 398R2 0.696 0.760 0.767

Notes: Outcome of interest is the (log) of indirect fire attacks dur-ing the post-harvest fighting season. We add one to all observa-tions before evaluating the logarithm. The quantity of interest isopium revenue for a given district-year. The regression is reducedform, using the primary instrument detailed in the IV section ofthe text. All regressions include district and fighting season fixedeffects as well as controls for the intensive margin of fighting duringthe fighting, harvest, and planting seasons respectively. Additionalparameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses.Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-21

Table A-9: Second stage effects of rebel capacity on production of indirect fire attacks

(1) (2) (3)Opium Revenue 0.0365∗∗∗ 0.0261∗∗ 0.0252∗∗

(0.0117) (0.0104) (0.0106)

Model ParametersFighting Season Fixed Effect Yes Yes YesFighting Season Activity (levels) Yes Yes YesGrowing Season Activity (levels) No Yes YesPlanting Season Activity (levels) No No YesModel StatisticsNo. of Observations 3582 3582 3582No. of Clusters 398 398 398R2 0.557 0.681 0.692

Notes: Outcome of interest is the (log) of indirect fire attacks dur-ing the post-harvest fighting season. We add one to all observationsbefore evaluating the logarithm. The quantity of interest is opiumrevenue for a given district-year. The regression displayed is thesecond stage, using the primary instrument detailed in the IV sec-tion of the text. All regressions include district and fighting seasonfixed effects as well as controls for the intensive margin of fight-ing during the fighting, harvest, and planting seasons respectively.Additional parameters are noted in the table footer. Heteroskedas-ticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-22

Table A-10: Impact of rebel capacity on within-day randomization of indirect fire attacks,excluding non-producers

(1) (2) (3) (4)Opium Revenue -0.139∗∗∗ -0.125∗∗∗ -0.116∗∗∗ -0.113∗∗∗

(0.0436) (0.0386) (0.0365) (0.0361)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 254 254 254 254No. of Clusters 70 70 70 70R2 0.151 0.185 0.213 0.217

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is opium revenue for a given district-year. All regressionsinclude fighting season fixed effects. Column 2-4 add controls for the intensivemargin of fighting during the fighting, harvest, and planting seasons respectively.Heteroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-23

Table A-11: Impact of rebel capacity on within-day randomization of indirect fire attacks,adjusting measure of revenue

(1) (2) (3) (4)Opium Revenue -0.139∗∗∗ -0.125∗∗∗ -0.116∗∗∗ -0.113∗∗∗

(0.0436) (0.0386) (0.0365) (0.0361)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 254 254 254 254No. of Clusters 70 70 70 70R2 0.150 0.185 0.213 0.217

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is opium revenue for a given district-year. All regressionsinclude fighting season fixed effects. Column 2-4 add controls for the intensivemargin of fighting during the fighting, harvest, and planting seasons respectively.Heteroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-24

A2.4 Additional IV Results

Aid delivery during growing season

Table A-12: Impact of rebel capacity on within-day randomization of indirect fire attacks,instrumental variables approach (second stage), accounting for aid delivery

(1) (2) (3)Opium Revenue -0.0741∗∗∗ -0.0743∗∗∗ -0.0725∗∗∗

(0.0247) (0.0247) (0.0234)

Model ParametersFighting Season Fixed Effect Yes Yes YesFighting Season Activity (levels) Yes Yes YesGrowing Season Activity (levels) Yes Yes YesPlanting Season Activity (levels) Yes Yes YesType of Aid No All CERP Agri./Irri. CERPModel StatisticsNo. of Observations 600 600 600No. of Clusters 154 154 154R2 0.173 0.173 0.180IV SpecificationIV Type Benchmark Benchmark BenchmarkKleibergen-Paap F Statistic 187.4 187.1 177.9

Notes: Outcome of interest is the (log) p-value of the randomness test. The quan-tity of interest is opium revenue for a given district-year instrumented using anopium suitability index interacted with the prior year’s national-level production(inverted). All regressions include fighting season fixed effects as well as con-trols for the intensive margin of fighting during the fighting, harvest, and plant-ing seasons respectively. Additional parameters are noted in the table footer.Heteroskedasticity robust standard errors clustered by district are reported inparentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-25

Baseline suitability specification

Table A-13: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, main estimating sample)

(1) (2) (3) (4)Suitability × Agg. Production 24.17∗∗∗ 24.20∗∗∗ 23.71∗∗∗ 23.72∗∗∗

(1.749) (1.763) (1.725) (1.732)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.465 0.467 0.472 0.473

Notes: Outcome of interest is opium revenue for a given district-year. Thequantity of interest is the opium suitability index interacted with the prioryear’s national-level production (inverted). All regressions include fightingseason fixed effects as well as controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Additionalparameters are noted in the table footer. Heteroskedasticity robust standarderrors clustered by district are reported in parentheses. Stars indicate ***p < 0.01, ** p < 0.05, * p < 0.1.

A-26

Table A-14: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, full panel sample)

(1) (2) (3) (4)Suitability × Agg. Production 20.54∗∗∗ 20.42∗∗∗ 20.04∗∗∗ 20.01∗∗∗

(1.093) (1.083) (1.073) (1.076)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 3582 3582 3582 3582No. of Clusters 398 398 398 398R2 0.304 0.304 0.310 0.311

Notes: Outcome of interest is opium revenue for a given district-year. Thequantity of interest is the opium suitability index interacted with the prioryear’s national-level production (inverted). All regressions include fightingseason fixed effects as well as controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Additionalparameters are noted in the table footer. Heteroskedasticity robust standarderrors clustered by district are reported in parentheses. Stars indicate ***p < 0.01, ** p < 0.05, * p < 0.1.

A-27

Table A-15: Impact of suitability instrument on within-day randomization of indirect fireattacks, instrumental variables approach (reduced form, main estimating sample)

(1) (2) (3) (4)Suitability × Agg. Production -1.917∗∗∗ -1.904∗∗∗ -1.758∗∗∗ -1.758∗∗∗

(0.666) (0.660) (0.594) (0.595)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.129 0.141 0.160 0.160

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is the opium suitability index interacted with the prioryear’s national-level production (inverted). All regressions include fighting sea-son fixed effects as well as controls for the intensive margin of fighting duringthe fighting, harvest, and planting seasons respectively. Additional parametersare noted in the table footer. Heteroskedasticity robust standard errors clus-tered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-28

Monotonicity assumption

Table A-16: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, main estimating sample) accounting for potential variation in instrumentcompliance via irrigation mechanism

(1) (2) (3) (4)Suitability × Agg. Production 23.72∗∗∗ 20.82∗∗∗ 23.52∗∗∗ 23.75∗∗∗

(1.732) (4.735) (2.492) (2.104)Irrigated Area: 75th pctl and above 7.407∗∗

(3.224)Suitability × Agg. Production × 75th 1.905

(4.893)Irrigated Area: 90th pctl and above 7.344

(5.400)Suitability × Agg. Production × 90th -2.039

(3.722)Irrigated Area: 95th pctl and above 13.45∗

(7.676)Suitability × Agg. Production × 95th -4.879

(4.781)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.473 0.494 0.481 0.487

Notes: Outcome of interest is opium revenue for a given district-year. The quantityof interest is the opium suitability index interacted with the prior year’s national-level production (inverted). All regressions include fighting season fixed effects aswell as controls for the intensive margin of fighting during the fighting, harvest,and planting seasons respectively. Additional parameters are noted in the tablefooter. Heteroskedasticity robust standard errors clustered by district are reportedin parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-29

Table A-17: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, full panel sample) accounting for potential variation in instrument com-pliance via irrigation mechanism

(1) (2) (3) (4)Suitability × Agg. Production 20.01∗∗∗ 16.84∗∗∗ 19.50∗∗∗ 19.89∗∗∗

(1.076) (1.953) (1.313) (1.201)Irrigated Area: 75th pctl and above 3.939∗∗

(1.564)Suitability × Agg. Production × 75th 4.595∗∗

(2.113)Irrigated Area: 90th pctl and above 0.186

(2.074)Suitability × Agg. Production × 90th 2.076

(1.975)Irrigated Area: 95th pctl and above 2.859

(2.879)Suitability × Agg. Production × 95th 0.0556

(2.231)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) Yes Yes Yes YesGrowing Season Activity (levels) Yes Yes Yes YesPlanting Season Activity (levels) Yes Yes Yes YesModel StatisticsNo. of Observations 3582 3582 3582 3582No. of Clusters 398 398 398 398R2 0.311 0.322 0.312 0.312

Notes: Outcome of interest is opium revenue for a given district-year. The quantityof interest is the opium suitability index interacted with the prior year’s national-level production (inverted). All regressions include fighting season fixed effects aswell as controls for the intensive margin of fighting during the fighting, harvest,and planting seasons respectively. Additional parameters are noted in the tablefooter. Heteroskedasticity robust standard errors clustered by district are reportedin parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-30

LASSO-based suitability specification

Table A-18: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, main sample, LASSO selection)

(1) (2) (3) (4)SuitabilityLASSO× Agg. Production 22.87∗∗∗ 22.88∗∗∗ 22.39∗∗∗ 22.39∗∗∗

(2.135) (2.150) (2.063) (2.059)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.429 0.431 0.435 0.436

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is the opium suitability index interacted with the prior year’snational-level production (inverted) where inputs are selected via LASSO. All re-gressions include fighting season fixed effects as well as controls for the intensivemargin of fighting during the fighting, harvest, and planting seasons respectively.Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate*** p < 0.01, ** p < 0.05, * p < 0.1.

A-31

Table A-19: Impact of suitability instrument on opium revenue, instrumental variables ap-proach (first stage, full panel sample, LASSO selection)

(1) (2) (3) (4)SuitabilityLASSO× Agg. Production 18.05∗∗∗ 17.92∗∗∗ 17.51∗∗∗ 17.49∗∗∗

(1.186) (1.168) (1.150) (1.150)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 3582 3582 3582 3582No. of Clusters 398 398 398 398R2 0.257 0.258 0.264 0.266

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantity of interest is the opium suitability index interacted with the prior year’snational-level production (inverted) where inputs are selected via LASSO. All re-gressions include fighting season fixed effects as well as controls for the intensivemargin of fighting during the fighting, harvest, and planting seasons respectively.Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate*** p < 0.01, ** p < 0.05, * p < 0.1.

A-32

Table A-20: Impact of suitability instrument on within-day randomization of indirect fireattacks, instrumental variables approach (reduced form, main sample, LASSO selection)

(1) (2) (3) (4)SuitabilityLASSO× Agg. Production -1.735∗∗∗ -1.731∗∗∗ -1.569∗∗∗ -1.569∗∗∗

(0.653) (0.645) (0.589) (0.589)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.111 0.124 0.143 0.143

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is the opium suitability index interacted with the prior year’s national-level production (inverted) where inputs are selected via LASSO. All regressionsinclude fighting season fixed effects as well as controls for the intensive margin offighting during the fighting, harvest, and planting seasons respectively. Additionalparameters are noted in the table footer. Heteroskedasticity robust standard errorsclustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-33

Agronomic inputs specification

Figure A-1: Estimated first stage effects of agronomic inputs on opium revenue.

-3

-2

-1

0

1

0-.05

0.5-1 1-2 2-3 3-4 4-5 5+

(a) Precipitation-Day Instruments

-10

-5

0

5

up to

270

270-2

75

275-2

80

280-2

85

285-2

90

290-2

95

295-3

00

300-3

05

305-3

10

310-3

15

(b) Temperature-Day Instruments

Notes: Results from Column 4 of Table A-21, where the outcome is opium revenue (as measured in the mainspecification) and the right hand side variables include the first stage instruments from our third IV strategy(raw agronomic inputs: precipitation-day (mm) and temperature-day (Kelvin) binned measures). Panel (a)plots the precipitation-day coefficients. Panel (b) displays the temperature-day coefficients.

A-34

Table A-21: Impact of agronomic instruments on opium revenue, instrumental variablesapproach (first stage, main sample, multiple IV approach)

(1) (2) (3) (4)Precip Days, 0-.05 -1.528∗∗∗ -1.533∗∗∗ -1.549∗∗∗ -1.548∗∗∗

(0.436) (0.436) (0.433) (0.434)Precip Days, 0.5-1 -1.583∗∗∗ -1.592∗∗∗ -1.618∗∗∗ -1.617∗∗∗

(0.489) (0.486) (0.483) (0.484)Precip Days, 1-2 -1.090∗∗ -1.112∗∗ -1.165∗∗ -1.164∗∗

(0.547) (0.554) (0.552) (0.554)Precip Days, 2-3 -1.409∗∗ -1.379∗∗ -1.397∗∗ -1.396∗∗

(0.674) (0.670) (0.666) (0.669)Precip Days, 3-4 -0.726 -0.747 -0.780 -0.780

(0.747) (0.748) (0.745) (0.746)Precip Days, 4-5 -1.214 -1.264∗ -1.306∗ -1.306∗

(0.767) (0.758) (0.753) (0.754)Precip Days, 5+ -1.166 -1.187 -1.083 -1.086

(0.874) (0.868) (0.857) (0.854)Temp Days, up to 270 -0.207∗ -0.216∗ -0.227∗∗ -0.227∗∗

(0.117) (0.116) (0.113) (0.112)Temp Days, 270-275 -0.284∗ -0.292∗ -0.298∗ -0.299∗

(0.158) (0.156) (0.153) (0.154)Temp Days, 275-280 -0.0866 -0.0924 -0.108 -0.109

(0.187) (0.186) (0.182) (0.181)Temp Days, 280-285 0.0702 0.0605 0.0423 0.0414

(0.127) (0.127) (0.125) (0.124)Temp Days, 285-290 0.108 0.0990 0.0817 0.0814

(0.193) (0.193) (0.189) (0.188)Temp Days, 290-295 -0.300 -0.304 -0.327 -0.327

(0.258) (0.258) (0.257) (0.257)Temp Days, 295-300 0.916∗∗∗ 0.912∗∗∗ 0.909∗∗∗ 0.910∗∗∗

(0.205) (0.204) (0.206) (0.205)Temp Days, 300-305 1.451∗∗∗ 1.454∗∗∗ 1.420∗∗∗ 1.418∗∗∗

(0.351) (0.352) (0.350) (0.357)Temp Days, 305-310 2.609∗∗ 2.628∗∗∗ 2.566∗∗ 2.567∗∗

(1.002) (1.006) (1.007) (1.007)Temp Days, 310-315 -1.431 -1.765 -1.332 -1.312

(3.158) (3.179) (3.130) (3.181)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.455 0.457 0.459 0.459

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantities of interest are the estimated effects of various precipitation-day andtemperature-day binned classifications. Precipitation is in millimeters and tem-perature is in Kelvin. All regressions include fighting season fixed effects as well ascontrols for the intensive margin of fighting during the fighting, harvest, and plant-ing seasons respectively. Additional parameters are noted in the table footer. Het-eroskedasticity robust standard errors clustered by district are reported in paren-theses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-35

Table A-22: Impact of agronomic instruments on opium revenue, instrumental variablesapproach (first stage, full panel sample, multiple IV approach)

(1) (2) (3) (4)Precip Days, 0-.05 -0.768∗∗∗ -0.748∗∗∗ -0.742∗∗∗ -0.738∗∗∗

(0.218) (0.218) (0.219) (0.219)Precip Days, 0.5-1 -0.795∗∗∗ -0.766∗∗∗ -0.766∗∗∗ -0.757∗∗∗

(0.246) (0.246) (0.247) (0.247)Precip Days, 1-2 -1.054∗∗∗ -1.008∗∗∗ -1.009∗∗∗ -1.001∗∗∗

(0.282) (0.283) (0.283) (0.283)Precip Days, 2-3 -1.048∗∗∗ -1.031∗∗∗ -1.023∗∗∗ -1.015∗∗∗

(0.267) (0.267) (0.268) (0.268)Precip Days, 3-4 -0.225 -0.196 -0.204 -0.207

(0.314) (0.315) (0.316) (0.316)Precip Days, 4-5 -0.675∗∗ -0.638∗∗ -0.652∗∗ -0.651∗∗

(0.294) (0.295) (0.294) (0.294)Precip Days, 5+ -0.738∗∗ -0.706∗ -0.646∗ -0.654∗

(0.371) (0.370) (0.370) (0.371)Temp Days, up to 270 -0.225∗∗∗ -0.224∗∗∗ -0.229∗∗∗ -0.231∗∗∗

(0.0663) (0.0664) (0.0660) (0.0660)Temp Days, 270-275 -0.194∗∗ -0.192∗∗ -0.198∗∗∗ -0.202∗∗∗

(0.0752) (0.0753) (0.0749) (0.0749)Temp Days, 275-280 -0.332∗∗∗ -0.336∗∗∗ -0.339∗∗∗ -0.343∗∗∗

(0.0936) (0.0936) (0.0927) (0.0929)Temp Days, 280-285 -0.0596 -0.0581 -0.0743 -0.0803

(0.0745) (0.0748) (0.0750) (0.0748)Temp Days, 285-290 -0.0811 -0.0786 -0.0916 -0.0934

(0.0793) (0.0797) (0.0791) (0.0789)Temp Days, 290-295 -0.127 -0.126 -0.137 -0.136

(0.109) (0.109) (0.109) (0.109)Temp Days, 295-300 0.381∗∗∗ 0.376∗∗∗ 0.384∗∗∗ 0.389∗∗∗

(0.121) (0.120) (0.120) (0.120)Temp Days, 300-305 0.857∗∗∗ 0.843∗∗∗ 0.793∗∗∗ 0.772∗∗∗

(0.193) (0.192) (0.191) (0.192)Temp Days, 305-310 1.320∗∗∗ 1.340∗∗∗ 1.268∗∗∗ 1.263∗∗∗

(0.407) (0.401) (0.396) (0.394)Temp Days, 310-315 8.374∗∗∗ 8.261∗∗∗ 9.125∗∗∗ 9.382∗∗∗

(3.033) (2.911) (2.863) (2.956)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 3582 3582 3582 3582No. of Clusters 398 398 398 398R2 0.204 0.206 0.213 0.214

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantities of interest are the estimated effects of various precipitation-day andtemperature-day binned classifications. Precipitation is in millimeters and tem-perature is in Kelvin. All regressions include fighting season fixed effects as well ascontrols for the intensive margin of fighting during the fighting, harvest, and plant-ing seasons respectively. Additional parameters are noted in the table footer. Het-eroskedasticity robust standard errors clustered by district are reported in paren-theses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-36

Table A-23: Impact of agronomic instruments on within-day randomization of indirect fireattacks, instrumental variables approach (reduced form, main sample, multiple IV approach)

(1) (2) (3) (4)Precip Days, 0-.05 0.0462 0.0442 0.0524 0.0525

(0.0795) (0.0788) (0.0793) (0.0794)Precip Days, 0.5-1 0.0443 0.0408 0.0543 0.0547

(0.0849) (0.0845) (0.0855) (0.0857)Precip Days, 1-2 0.0484 0.0393 0.0666 0.0668

(0.0898) (0.0873) (0.0877) (0.0877)Precip Days, 2-3 0.0784 0.0905 0.100 0.100

(0.117) (0.113) (0.111) (0.112)Precip Days, 3-4 0.107 0.0986 0.115 0.115

(0.143) (0.143) (0.148) (0.148)Precip Days, 4-5 0.115 0.0950 0.116 0.116

(0.109) (0.108) (0.108) (0.108)Precip Days, 5+ -0.0768 -0.0850 -0.138 -0.139

(0.210) (0.210) (0.202) (0.202)Temp Days, up to 270 0.0237 0.0203 0.0260 0.0259

(0.0178) (0.0172) (0.0172) (0.0172)Temp Days, 270-275 0.0420∗ 0.0388∗ 0.0421∗ 0.0420∗

(0.0233) (0.0230) (0.0227) (0.0230)Temp Days, 275-280 0.0369 0.0346 0.0425∗ 0.0424∗

(0.0248) (0.0243) (0.0249) (0.0251)Temp Days, 280-285 0.0193 0.0154 0.0247 0.0245

(0.0217) (0.0216) (0.0221) (0.0226)Temp Days, 285-290 0.0206 0.0169 0.0258 0.0257

(0.0288) (0.0283) (0.0263) (0.0263)Temp Days, 290-295 0.0832∗∗ 0.0817∗∗ 0.0937∗∗ 0.0937∗∗

(0.0402) (0.0400) (0.0416) (0.0416)Temp Days, 295-300 0.00547 0.00387 0.00505 0.00512

(0.0344) (0.0339) (0.0339) (0.0341)Temp Days, 300-305 -0.171∗∗ -0.171∗∗ -0.154∗∗ -0.154∗∗

(0.0750) (0.0738) (0.0739) (0.0747)Temp Days, 305-310 -0.607∗ -0.600∗∗ -0.568∗∗ -0.568∗∗

(0.308) (0.303) (0.284) (0.284)Temp Days, 310-315 3.420∗∗∗ 3.285∗∗∗ 3.063∗∗∗ 3.067∗∗∗

(1.013) (0.988) (0.907) (0.914)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 600 600 600 600No. of Clusters 154 154 154 154R2 0.149 0.160 0.183 0.183

Notes: Outcome of interest is the (log) p-value of the randomness test. Thequantities of interest are the estimated effects of various precipitation-day andtemperature-day binned classifications. Precipitation is in millimeters and tem-perature is in Kelvin. All regressions include fighting season fixed effects aswell as controls for the intensive margin of fighting during the fighting, harvest,and planting seasons respectively. Additional parameters are noted in the ta-ble footer. Heteroskedasticity robust standard errors clustered by district arereported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-37

A2.5 Additional Heterogeneous Effects: Intelligence Gathering

Table A-24: Heterogeneous effects of rebel capacity on within-day randomization of indirectfire attacks with respect to potential intelligence gathering via security base breaches

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0564∗∗∗ -0.0574∗∗∗ -0.0537∗∗∗ -0.0537∗∗∗

(0.0137) (0.0143) (0.0141) (0.0131) (0.0131)Infiltration 0.888∗∗∗ 0.740∗∗∗ 0.760∗∗ 0.761∗∗

(0.239) (0.257) (0.307) (0.307)Infiltration × Revenue -0.0418∗∗∗ -0.0350∗∗ -0.0308∗ -0.0308∗

(0.0131) (0.0146) (0.0160) (0.0161)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.157 0.173 0.188 0.188

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-38

Table A-25: Heterogeneous effects of rebel capacity on within-day randomization of indirectfire attacks with respect to potential intelligence gathering via insider attacks

(1) (2) (3) (4) (5)Opium Revenue -0.0581∗∗∗ -0.0461∗∗∗ -0.0470∗∗∗ -0.0433∗∗∗ -0.0433∗∗∗

(0.0137) (0.0110) (0.0111) (0.00921) (0.00920)Insiders -2.026 -1.924 -1.868 -1.861

(1.479) (1.385) (1.526) (1.511)Insiders × Revenue -0.0932∗∗∗ -0.0899∗∗∗ -0.0903∗∗∗ -0.0909∗∗∗

(0.0302) (0.0296) (0.0335) (0.0344)

Model ParametersFighting Season Fixed Effect Yes Yes Yes Yes YesFighting Season Activity (levels) No No Yes Yes YesGrowing Season Activity (levels) No No No Yes YesPlanting Season Activity (levels) No No No No YesModel StatisticsNo. of Observations 600 600 600 600 600No. of Clusters 154 154 154 154 154R2 0.154 0.256 0.263 0.278 0.278

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantity of interest isopium revenue for a given district-year. All regressions include fighting season fixed effects as wellas controls for the intensive margin of fighting during the fighting, harvest, and planting seasonsrespectively. Additional parameters are noted in the table footer. Heteroskedasticity robuststandard errors clustered by district are reported in parentheses. Stars indicate *** p < 0.01, **p < 0.05, * p < 0.1.

A-39

A2.6 Additional Heterogeneous Effects: Labor Scarcity

Table A-26: Effects of rebel capacity and battlefield losses on within-day randomization ofindirect fire attacks, accounting for counterinsurgent operations from Tables A-3 and A-4]

(1) (2) (3)Opium Revenue -0.0191∗∗∗ -0.0200∗∗∗ -0.0215∗∗∗

(0.00574) (0.00698) (0.00670)Battlefield Losses 0.0486∗∗ 0.0828∗∗∗

(0.0207) (0.0274)

Model ParametersFighting Season (FS) Fixed Effect Yes Yes YesFS Activity (levels) No Yes YesGrowing Season Activity (levels) No Yes YesPlanting Season Activity (levels) No Yes YesFS Combat Operations (all, levels) Yes Yes NoFS COIN Operations (all, levels) No No YesModel StatisticsNo. of Observations 600 600 600No. of Clusters 154 154 154R2 0.496 0.506 0.542

Notes: Outcome of interest is the (log) p-value of the randomness test.The quantity of interest is opium revenue for a given district-year. Allregressions include fighting season fixed effects as well as controls for theintensive margin of fighting during the fighting, harvest, and plantingseasons respectively. Additional parameters are noted in the table footer.Fighting season parameters are notated with the abbreviation FS. Bat-tlefield losses in our sample have a mean of 4.605 and standard deviationof 10.547. Heteroskedasticity robust standard errors clustered by districtare reported in parentheses. Stars indicate *** p < 0.01, ** p < 0.05, *p < 0.1.

A-40

A2.7 Varying Control over Attack Timing

As we describe in the main text, insurgents have varying levels of control over the timing oftheir attacks. Indirect fire events can be initiated at any time against stationary targets likebases or military outposts. The timing of direct fire and IED attacks cannot be controlledunilaterally by rebels. Close combat, for example, is often characterized by attacks onconvoys and non-stationary targets. Troops and vehicles are rotated from locations on non-random schedules. The timing of these attacks, therefore, is consistently less random as aconsequence of government strategy, not rebel tactics. Similarly, IEDs may be emplacedhours or days before they are triggered by a passing convoy. Rank ordered, rebels have theleast control over the timing of roadside bomb attacks.

We replicate the visual evidence we introduce in our main results in Figures A-2 and A-3.Notice that direct fire, over which insurgents maintain some limited control over timing, isnegatively correlated with revenue but the slope is consistently flatter than for indirect fireattacks (over which rebels have unilateral timing control). For IEDs, the coefficient is effec-tively zero. We introduce the regression-based evidence in Tables A-27 and A-28. Althoughdirect fire attacks are consistently negatively correlated with revenue, the magnitude of themain effect (when compared to our indirect fire results) is consistently weaker. Similarly,although our point estimates are consistently negative with respect to roadside bombs, ourprecision is substantially diminished. These results are consistent with our main effects sincerebels lack the ability to control the timing of these other attack types.

A-41

Figure A-2: Bivariate relationship between opium revenue and p-value of randomization testof combat (direct fire attacks) in Afghanistan

0

20

40

60

80

Opi

um re

venu

e

-20 -15 -10 -5 0Logarithm of p-values from KS test -- Direct Fire Attacks

Observed opium revenue/p-value Fit line with 95% CI

Figure A-3: Bivariate relationship between opium revenue and p-value of randomization testof combat (IED attacks) in Afghanistan

0

20

40

60

80

Opi

um re

venu

e

-15 -10 -5 0Logarithm of p-values from KS test -- IED Attacks

Observed opium revenue/p-value Fit line with 95% CI

A-42

Table A-27: Impact of rebel capacity on within-day randomization of direct fire attacks

(1) (2) (3) (4)Opium Revenue -0.0309∗∗∗ -0.0110∗∗∗ -0.0121∗∗∗ -0.0119∗∗∗

(0.00780) (0.00292) (0.00328) (0.00327)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 1128 1128 1128 1128No. of Clusters 236 236 236 236R2 0.0963 0.448 0.450 0.464

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fightingseason fixed effects. Column 2-4 add controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Heteroskedasticityrobust standard errors clustered by district are reported in parentheses. Stars indi-cate *** p < 0.01, ** p < 0.05, * p < 0.1.

A-43

Table A-28: Impact of rebel capacity on within-day randomization of IED attacks

(1) (2) (3) (4)Opium Revenue -0.00849∗∗ 0.000559 -0.000232 -0.00000219

(0.00385) (0.00259) (0.00280) (0.00270)

Model ParametersFighting Season Fixed Effect Yes Yes Yes YesFighting Season Activity (levels) No Yes Yes YesGrowing Season Activity (levels) No No Yes YesPlanting Season Activity (levels) No No No YesModel StatisticsNo. of Observations 653 653 653 653No. of Clusters 161 161 161 161R2 0.0700 0.179 0.186 0.186

Notes: Outcome of interest is the (log) p-value of the randomness test. The quantityof interest is opium revenue for a given district-year. All regressions include fight-ing season fixed effects. Column 2-4 add controls for the intensive margin of fightingduring the fighting, harvest, and planting seasons respectively. Heteroskedasticity ro-bust standard errors clustered by district are reported in parentheses. Stars indicate*** p < 0.01, ** p < 0.05, * p < 0.1.

A-44